Augustin, Michael J., Self-Instantiation in Plato's Parmenides and Sophist

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UNIVERSITY OF CALIFORNIA

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Self-instantiation in Plato’s Parmenides and Sophist

A dissertation submitted in partial satisfaction of the

requirements for the degree Doctor of Philosophy

in Philosophy

Michael James Augustin

Committee in charge:

Professor Voula Tsouna, Chair

Professor Richard McKirahan

Professor Richard Bett

Professor Thomas Holden

June 2018

The dissertation of Michael James Augustin is approved.

______Thomas Holden

______Richard Bett

______Richard McKirahan

______Voula Tsouna, Committee Chair

June 2018

Self-instantiation in Plato’s Parmenides and Sophist

Michael James Augustin

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For my late grandfather, Irwin Lee Klundt

He was a philosopher in the true sense of the word, a “lover of wisdom,” and told me that my graduate studies would be “the most enjoyable time of your entire life.”

You were not wrong, Grandpa.

VITA OF MICHAEL JAMES AUGUSTIN June 2018

EDUCATION

Bachelor of Arts in Philosophy, Arizona State University, May 2009 (summa cum laude) Master of Arts in Philosophy, Georgia State University, May 2012 Doctor of Philosophy in Philosophy, University of California, Santa Barbara, June 2018 (expected)

PROFESSIONAL EMPLOYMENT

2012-13: Teaching Assistant, Department of Philosophy, University of California, Santa Barbara Summer 2013: Teaching Associate, Department of Philosophy, University of California, Santa Barbara 2013-15: Teaching Assistant, Department of Philosophy, University of California, Santa Barbara 2015-16: Teaching Associate, Department of Philosophy, University of California, Santa Barbara Spring 2016: Teaching Assistant, Department of Philosophy, University of California, Santa Barbara Fall 2017: Teaching Assistant, Department of Philosophy, University of California, Santa Barbara Winter 2018: Teaching Associate, Department of Philosophy, University of California, Santa Barbara Spring 2018: Teaching Assistant, Department of Philosophy, University of California, Santa Barbara

PUBLICATIONS

“Epicureanism and the Health of the Soul,” In Ancient Thought, edited by Nathan J. Barnes, Josh Carroll, Oliver Langworthy, and Erlend MacGillivary. 2017.

“Weight in Greek Atomism,” Philosophia, 45 (2015), 76-99.

AWARDS

Academic Senate’s Doctoral Student Travel Grant, University of California, Santa Barbara, 2018

Charlotte Stough Memorial Prize, University of California, Santa Barbara, 2017

Regents Special Fellowship, University of California, Santa Barbara, 2016

Graduate Student Association’s Travel Grant, University of California, Santa Barbara, 2016

Paul Wienpahl Award for Teaching Excellence, University of California, Santa Barbara, 2016

Graduate Student Association’s Travel Grant, University of California, Santa Barbara, 2015 Charlotte Stough Memorial Prize, University of California, Santa Barbara, 2013

Graduate Student Association’s Travel Grant, University of California, Santa Barbara, 2013

Regents Special Fellowship, University of California, Santa Barbara, 2012

Phi Sigma Tau (Zeta) — Scholar Travel Stipend, Georgia State University, 2012

Philosophy Department’s Professional Development Travel Grant, Georgia State University, 2011

Phi Sigma Tau (Zeta) — Scholar Travel Stipend, Georgia State University, 2011

Sun Angel Excellence in the Humanities Research Scholarship, Arizona State University, 2008

FIELDS OF STUDY

Major Field: Ancient Philosophy

ABSTRACT

Self-instantiation in Plato’s Parmenides and Sophist

Michael James Augustin

The present project brings together two areas of Platonic scholarship. One area is Plato’s

Parmenides, the dialogue that appears to cripple the theory of Forms. Yet though the theory meets with several seemingly devastating criticisms, Parmenides himself tells the young

Socrates that it is in fact possible to save the Forms. Scholars are divided over just how, if at all, this rescue happens.

The other area concerns “self-predication,” a particular sort of predication displayed in statements of the form “the F is F,” where the subject term names some Form. Scholars are divided here too, and in two ways. First, there is disagreement about just how we should understand the very notion of self-predication. What does a statement of the form “the F is

F” even mean? Second, there is debate over whether Plato himself endorses (or should endorse) some particular understanding of self-predication.

My focus here is an interpretation of self-predication on which statements of the form

“the F is F” say that the Form is characterized by the very quality it constitutes, or “self- instantiates” as I will often put it. The majority position in the literature is that Plato no longer subscribes to (or should no longer subscribe to) this particular understanding of self- predication after the Parmenides. The reason is simple: self-predication understood in this

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way is largely responsible for the theory of Forms’ being sunk in the Parmenides. Saving the theory of the Forms requires, it is often claimed, jettisoning from the theory this special sort of predication.

I find myself part of a small group of scholars that reject the majority positon. My own reading is that self-instantiation, far from sinking the theory of Forms in the Parmenides, is essential for saving the theory from Parmenides’s criticisms; the theory survives into the late dialogues largely because of this special sort of predication. In addition, I maintain that Plato himself was aware of how to disarm the objections presented in the dialogue, that self- instantiation plays this important role, and that the arguments are marshalled in part to compel us, his readers, to appreciate this for ourselves.

The chapters that follow are principally concerned with the former part of my position, establishing the importance of self-instantiation for the theory of Forms post-Parmenides. I shall at times say some things about the latter, but it does not receive a full defense here.

Still, I believe that it is nonetheless important to state this part of my view too.

Chapters I and II focus on a pair of regress arguments from the Parmenides. It is widely thought that these arguments are successful precisely because of self-instantiation, and that the only way to disarm them is by dispensing with this tenet of the theory of Forms. I argue that this is wrong for both arguments, and offer alternative interpretations of them.

Collectively, Chapters I and II show us that we must take seriously questions concerning how some Forms are characterized by the very qualities they constitute, and why this special sort of predication is part of the theory of Forms.

Chapter III engages with the Parmenides’s bewildering dialectical display, which is said to be the method of training that will allow a young Socrates to save the theory of Forms. I consider and reject a prominent interpretation of the exercise, and then develop my own that

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sheds light on the importance of self-instantiation, reinforces earlier conclusions, and paves the way for consideration of Plato’s Sophist. It is in this dialogue, I maintain, that we find answers to the how and why questions.

Chapter IV answers these questions. I argue that some Form is an instance of itself just in case that Form participates in itself. In addition, I show that self-participation, and so self- instantiation, is limited to certain Forms. These conclusions naturally invite consideration of the why question. Here my position is that some Form participates in itself just in case that

Form plays a “structuring role” in the intelligible and sensible realms. Chapter V considers a question raised by this answer, namely, Does the Form of Change play a structuring role in the intelligible realm? If so, then the Forms, after the Parmenides, lose their immutability.

This, interestingly, is another majority position in the literature. I side with the minority once more, arguing that the Form of Change does not play a structuring role in the intelligible realm. The result is that whatever changes the theory of Forms undergoes following its critique in the Parmenides, self-instantiation remains part of the theory and the Forms are still stable, unchanging entities.

I. Parmenides’s initial regress argument

A. Introduction

This chapter is concerned with Parmenides’s third criticism of the theory of Forms.1 It is often called “the Third Man Argument,” but I shall refer to it as “Parmenides’s initial regress argument.” The argument’s success requires that the Forms are characterized by the very qualities they constitute or “self-instantiate.” The dominant response in the scholarly literature is that Plato should jettison this tenet from the theory of Forms — the assumption here is that Plato did not know how to prevent the regress — or that he is here signaling that this tenet is to be jettisoned — the assumption here is that he did know how to prevent the regress. Whichever is ultimately the case, it is widely maintained that the lesson to be learned from this argument is that the Forms no longer self-instantiate.

Here I shall argue against this line of response. My argument is straightforward: this cannot be the argument’s lesson because some Forms must be characterized by the very qualities they constitute. Specifically, those Forms that I call the “structuring Forms.”2 I maintain that Plato himself is aware of this — the entire critique of the theory of Forms in this dialogue’s first part is too precise — and that he uses this argument to encourage his reader to consider how and why some Forms are characterized by the very qualities they constitute. Answers to these questions, I shall show in Chapters III and IV, are found in the

Parmenides’s second part and central sections of the Sophist. Finally, I shall explore the

1 I understand Parmenides’s first criticism to concern the extent of the Forms (130a8-e5), and that his second is the “Whole/Part dilemma” (130e6-131e7). Unless I indicate otherwise, all references are to the Parmenides.

2 This class of Forms is discussed at length in Chapter IV.

possibility that we should reject the “Non-Identity Assumption” (NI) in order to prevent the generation of Parmenides’s regress.

B. Parmenides’s argument

Let us begin with a review of the Parmenides’s initial regress argument. Parmenides says to Socrates,

I suppose you believe that each Form is one (hen hekaston eidos ... einai) for the

following reason: whenever a number of things appear to you to be large, it would seem

that the one and the same character (mia ... idea hê autê) applies to all of them; therefore,

you would presume that the Large is one (hen to mega ... einai). (132a1-3)3

Here Parmenides offers a reason for Socrates’s belief that each Form is one (hen).4 That is, that there is one and only one Form corresponding to some character (of the appropriate sort).5 When Socrates introduces the Forms earlier in this dialogue — in response to an argument from Zeno against the position that polla esti ta onta — he certainly assumes that this is so. What is not provided (at least, explicitly) is some reason that justifies that there is one and only one Form corresponding to some character (of the appropriate sort). So,

3 All references are to the Parmenides unless I indicate otherwise.

4 The notion of “one” (hen) here is robust, capturing both unity and uniqueness. Thus, I remain convinced by the arguments in Vlastos (1969) 293-7, despite the efforts of others against this reading (see for instance Fine (1993) 208-10). However, that “oneness” is a robust notion in the Parmenides does not entail that any particular argument in this dialogue targets it as a whole. This initial regress argument challenges the uniqueness of the Forms, while the argument at 131a5-e7, often called “the Whole/Part dilemma,” sets its sights on the unity of the Forms.

5 This parenthetical is required in the light of Socrates’s earlier uncertainty concerning the extent of the Forms (130a3-e4).

Parmenides offers a reason: whenever Socrates surveys some number of things that are, say, large, it seems to him that they exhibit the one and the same character, largeness. Since, on

Socrates’s view, perceptible things exhibit some character or other through participation in the relevant Form, and each of these perceptible things exhibits one and the same character, in this case “largeness,” all of them participate in the one and the same Form. Consequently,

Socrates believes that the Large itself (indeed that each Form) is one.

It has become commonplace to generalize this reason offered by Parmenides.6 We may refer to it as “the One-Over-Many Assumption” (OM),

(OM) For any group of things exhibiting some character (of the appropriate sort) in

common, there is one Form that accounts for the exhibition of that character

by each of the things in that group.

Socrates explicitly accepts Parmenides’s proposed reason. Parmenides then continues,

Yet what about the Large itself and the other things that are large? If you regard all

things the same way in your mind’s eye (ean hôsautôs tê psuchê epi panta idês), will not

yet again one large thing make its appearance by which all those things necessarily

appear large? — So it would seem. — So, another Form of Largeness will appear again

alongside the Largeness that has come to be and the things that partake in it; and, in

addition to all those still another by reason of which all those will be large. So, each of

6 This generalization of the argument’s first premise understands the argument as applicable to all Forms, not just the Form of Largeness that Parmenides focuses on here. However, see Allen (1997) 157-158 who denies that the argument is generalizable to all Forms.

your Forms will no longer be one (ouketi ... hen hekaston soi tôn eidôn estai), but

unlimited in multitude (apeira to plêthos). (132a5-b2)

Here Parmenides considers the consequences of applying (OM) to a new group of large things. Namely, the original group of large things in the argument’s initial stage and the

Form of Largeness because of which (that is, through participation) those things are large.

Socrates agrees with Parmenides that (OM), when applied to this new group of large things, will result in the appearance of another Largeness, because of which (that is, through participation) this expanded group of large things is large. This application of (OM) to an expanded group of large things is, unfortunately for Socrates, repeatable indefinitely. Thus

(OM), far from securing the oneness of the Large itself, undermines it by yielding a plurality of Largenesses. As Parmenides puts it, each Form is no longer one but unlimited in multitude.

Why does Socrates agree with the conclusions drawn by Parmenides in this argument’s second stage? Parmenides does indeed invite Socrates to view the Large itself and the other large things together, in the same way, with his mind’s eye. But why does this cause

Socrates to admit that there will appear another Form of Largeness? It must be that

Parmenides’s invitation capitalizes on Socrates’s implicit commitment to certain assumptions, which are then used to undermine his belief that each Form is one. Which assumptions? The now (in)famous “Self-Instantiation Assumption” (SI) and “Non-Identity

Assumption” (NI),7

7 (SI) is often called the “Self-Predication Assumption” (SP). Since my concern here is a special sort of self-predication, one where the Form is characterized by the very quality it constitutes (or “self-instantiates”), I depart from the common name for this assumption.

(SI) Any Form that accounts for the exhibition of a common character by some

group of things itself exhibits that character.

(NI) No Form that accounts for the exhibition of a common character by some

group of things is itself part of that group.

Armed with these two assumptions, Parmenides can demonstrate that each Form is unlimited in multitude.8 After the argument’s initial stage, he reasons that by (SI) the Form of Largeness is itself a large thing. Therefore, it can be grouped with some set of large things that are large through their participation in the Large itself. But if the Form of Largeness is grouped with some set of large things, then by (NI) it cannot account for the largeness exhibited by this set of things. For it itself is a member of this group. Consequently, by

(OM) another (that is, a second) Form of Largeness must come into view “over and above” this group of large things that includes the already-present Form of Largeness. Since this second Form of Largeness is not a member of that group of large things, it is not identical with the original Form of Largeness that is a member of this group. In addition, it is this second Form of Largeness that now accounts for the largeness exhibited by those perceptible things constitutive of the original group of large things. For the original set is itself a subset of this new set of large things. Now by (SI) this second Form of Largeness is itself a large thing. So, it too may be viewed in the same way through the mind’s eye as a member in the set of large perceptible things and the original Form of Largeness. By (NI), this second Form of Largeness cannot account for the largeness exhibited by this expanded group of large

8 Not all scholars agree on this point. The more notable dissenting studies include Pickering (1981) and Mann (1979). Both of these scholars deny that Parmenides’s initial regress argument requires the Self-Instantiation Assumption and the Non-Identity Assumption. Sharvy (1986) denies that the argument requires the Non-Identity Assumption.

things. For it itself is a member of that group. Therefore, by (OM) a third Form of Largeness must come into view “over and above” this group of large things and so on ad infinitum. As a result, (OM) when conjoined with (SI) and (NI) undermines Socrates’s belief that the

Large itself (indeed that each Form) is one.

C. Possible lines of response

How could Plato respond to this argument, preventing the regress that undermines the oneness of the Forms?

One line of response would challenge that the Forms are characterized by the very qualities they constitute. Naturally, then, its answer to the above question focuses on (SI).

The role of this assumption in the argument is securing that the Form of Largeness itself is a large thing, and that it is large in the same way that each member in some group of perceptible large things is large. Since the Large itself is large in the same way that each member in some group of perceptible large things is large—that is, all of them exhibit the same character—the Large itself can become a member of that group. But when it does, and as we saw, another Form of Largeness must appear because of (OM) and (NI). If the Large itself exhibits the same character as each member in this group of perceptible large things, then just as each member of this group is large through participation in something else

(namely, the Large itself), so too is each member in this expanded group of large things, which includes the Large itself, large through participation in something else (namely, a second Form of Largeness). The same type of explanation, that is, must hold for both groups. But the appearance of this second Form of Largeness can be blocked by preventing the original Form of Largeness from joining as a member some group of perceptible large things. How so? Reject (SI), and reinterpret statements of the form “the F is F.” However

this is done, its effect is that the statement “the Large itself is large” is not true under the same conditions that the statement “Wilbur the cat is large” is true.9 For in whatever way that the Large itself is large, it is not large in the same way that Wilbur the cat is large. As a result, the Large cannot join some group of perceptible large things simply in virtue of being large. Consequently, a step central to the Parmenides’s initial regress argument is blocked.

Another line of response maintains that although there is a sense in which the Large itself is large in the same way as each member in some group of perceptible large things— that is, all of them exhibit the same character—there is another sense in which the Large itself is large that is not the same as the way in which each member in some group of perceptible large things is large. What is this “other sense”? While each member in some group of perceptible large things is large through participation in the Large itself, it is not the case that, even when grouped with this set of perceptible large things, the Large itself is large through participation in something else (say, another Form of Largeness). While the character exhibited by these perceptible things and the Large itself is the same, the explanation for why each thing exhibits that same character is not the same.

9 A few different reinterpretations are found in the secondary literature. Cherniss (1957), for instance, maintains that these statements are in fact identity statements. Peterson (1973) explores so-called “Pauline Predications” in relation to Parmenides’s initial regress argument. For a different application of Pauline Predications, see Vlastos (1973) 221-65, 270-322. Nehamas (1982), argues that statements of this form in fact describe the Form’s nature. That is, the statement “the Large itself is large” means “the Large itself is the what it is to be large.” Note that Nehamas’s contention that statements of the form “the F is F” in fact describe a Form’s nature does not thereby commit him to a view where the Form exhibits its nature. That is, maintaining that the statement “the Large itself is large” means “the Large itself is the what it is to be large” does not then entail that the Large itself exhibits the character of largeness. This latter is so only if a Form participates in itself. On these points see especially Nehamas (1982) 352-58. Below I discuss in some detail Meinwald (1991), which distinguishes between two kinds of predications and contends that these are central to the second part of the Parmenides. While I find some aspects of Meinwald’s proposal compelling, I shall argue that it meets with at least one serious difficulty.

Naturally, then, this alternative line of response focuses on either (OM) or (NI). In addition, it maintains that one of these assumptions is responsible for Socrates’s predicament. Consider (OM). The role of this assumption in the argument is explaining why each member in some group of large things is large.10 When the group in question consists solely of perceptible large things, (OM) explains why each member of this group is large through its participation in the Large itself. But when this group also includes the Large itself, the result, due to (NI), is that another Form of Largeness must appear to explain why each member of this expanded group is large. As I wrote above when presenting the first line of response, it seems that the same type of explanation — participation in something else — must hold for both groups. Hence the first line of response contending that the assumption responsible for Socrates’s predicament is (SI), and its assertion that (SI) should be rejected. Instead of denying, though, that the Large itself exhibits the same character as the perceptible large things partially constitutive of this expanded group, the appearance of this second Form of Largeness can be blocked in another way. Specifically, by contending that as formulated (OM) is too general — it does not distinguish between perceptible things,

10 It is not clear that this is Plato’s only use of (OM). Consider, for instance, the questions that Parmenides puts to Socrates at 130b2-e4. Here Socrates readily asserts that there are Forms of Likeness, Oneness, Multitude, Justice, Beauty, and Goodness (among others). He is hesitant about the Form of Human Being, the Form of Fire, and the Form of Water, and outright rejects the existence of Forms for hair, mud, dirt, and anything else altogether worthless and base (atimotaton te kai phaulotaton). Then Socrates admits that he is “troubled at times whether the same should not apply in all cases.” It is arguable that “the same” (tauto) here refers to (OM). If so, then (OM) is used in this line of questioning as a reason for positing the existence of certain Forms. That is, if (OM) posits the existence of Oneness or Justice, then, presses Parmenides, why not more mundane things such as hair or mud? But even if (OM) is used elsewhere as a reason for positing the existence of certain Forms—something about which I am doubtful; for an especially stimulating discussion of this issue see Sedley (2013)—it is certainly not used in this way in Parmenides’s initial regress argument. The existence of Forms is granted by Parmenides (consider too their introduction by Socrates at 128e7-129a3 and Parmenides declaration of their necessity at 135b6-c7). The issue is whether (OM) can serve as justification for Socrates’s belief that each Form is one.

on the one hand, and Forms, on the other. An appropriately restricted (OM) by this answer would read, “For any group of perceptible things exhibiting some character (of the appropriate sort) in common, there is one Form that accounts for the exhibition of that character by each of the perceptible things in that group.” When each member in some group of large things is a perceptible thing, the group requires one Form over and above it that accounts for each member of this group’s being large, namely the Large itself.

However, if the Large itself is also a member in this group of large things, it does not require

(as perceptible things do) another Form of Largeness over and above it to account for its largeness. Put differently the Form of Largeness (indeed all other Forms) is exempt from

(OM); it is not subject to the same type of explanation for its being large. Consequently, a step central to Parmenides’s initial regress argument is blocked.

Consider now (NI). Recall that (NI) states, “No Form that accounts for the exhibition of a common character by some group of things is itself part of that group.” The role of this assumption in the argument is determining when the Large itself can fulfill a particular role: explaining why each member in some group of large things is large. (NI) asserts that the

Large itself can fulfill this explanatory role only when it is not grouped with some set of large things that participate in it. Put differently, by (SI) the Large itself is a large thing. As such it can be grouped with some set of perceptible large things, each of which is large through its participation in the Large itself. But when the Large itself is grouped with these perceptible large things, as Parmenides invites Socrates to do in the argument’s second stage, the result given (NI) is that no longer can the Large itself explain why those large things constitutive of this group are large. By (OM) another (that is, a second) Form of

Largeness now appears, and it supplies the requisite explanation for why each member in this group of large things is large. But the appearance of this second Form of Largeness can

be blocked in yet another way: rejecting (NI). If (NI) is rejected, then the Large itself always fulfills its explanatory role regardless of whether it is (or is not) grouped with some set of large things that participate in it. The original Form of Largeness never abandoned its

“explanatory post,” so to speak. Thus, there is no reason for another Form of Largeness to appear and fill this explanatory role. Consequently, a step central to Parmenides’s initial regress argument is blocked.

D. Which line of response?

From the foregoing, it is clear that engaging with either (SP), (OM), or (NI) is sufficient for preventing the regress central to Parmenides’s argument. I maintain that Plato does not consider either (SI) or (OM) to be the problematic assumption. Rather, it is (NI) that is the problematic assumption. I consider both (SI) and (OM) in the sections that follow, showing that engaging with either of these assumptions does not agree with what the learn about the future of the theory of Forms in the Sophist. This leaves only (NI). I explore why this is the problematic assumption below, focusing in particular on the notion of explanation.

E. Self-instantiation (SI)

We begin with (SI). Recall that it reads,

(SI) Any Form that accounts for the exhibition of a common character by some

group of things itself exhibits that quality.

An answer to Parmenides’s initial regress argument that focuses on this assumption argues that it should be rejected, and that we reinterpret statements of the form “the F is F.”

However this is done, its effect is that the statement “the Large itself is large” is not true

under the same conditions that the statement “Wilbur the cat is large” is true. For in whatever way that the Large itself is large, it is not large in the same way that Wilbur the cat is large. As a result, the Large cannot join some group of perceptible large things simply in virtue of being large. Consequently, a step central to Parmenides’s initial regress argument is blocked.

Several versions of this assumption are found in the secondary literature. I cannot discuss all of them here. I shall, then, confine myself to a recent reinterpretation that has found favor in the secondary literature. This is Constance Meinwald’s approach presented and defended at length in her monograph on the Parmenides.11 Before presenting the core of

Meinwald’s approach, though, I shall provide some necessary stage-setting by discussing a section of the dialogue that we may call “Parmenides’s transitional remarks” (134e7-136c5).

After presenting a series of seemingly devastating criticisms to Socrates’s position,

Parmenides states that these and many more difficulties are inseparable from the Forms insofar as these are “the things that are” (tôn ontôn) and each of them is “defined … as something by itself” (horieitai tis auto). Still, their existence cannot be denied. For if the existence of the Forms is denied, then no longer are there objects of thought (dianoia) and the power of discourse has been completely destroyed (tên tou dialegesthai dunamin pantapasi diaphtherei). Overcoming these difficulties, Parmenides continues, requires engaging in a particular method of training. This method was demonstrated in part by Zeno

11 See Meinwald (1991), especially 46-75. Some of the monograph’s central contentions are summarized and applied to Parmenides’s initial regress argument and “the Greatest Difficulty” (133b5-134e7), the last argument marshaled by Parmenides against Socrates’s position, in Meinwald (1992). Meinwald’s approach has been adopted, developed, and defended in Peterson (1996), (2000), and (2003), and a version of this approach is at work in Kahn (2013). For a more recent defense in conjunction with some comparisons to other views, see Meinwald (2014).

earlier in their conversation. But Socrates himself must go beyond Zeno’s demonstration in at least two ways. First, Socrates must not concern himself with the perceptible things but only with those things one could apprehend best by reasoning (ha malista tis an logô laboi) and could call “Forms” (eidê an hêgêsaito einai). Second, he must consider both what follows if a particular hypothesis is true and what follows if a particular hypothesis is not true. Parmenides then expands upon this latter by way of Zeno’s thesis that ei polla esti before summing up the method of training in this way: whatever Socrates hypothesizes as either being or not being (hôs ontos kai ôs ouk ontos), or subject to any other qualification whatsoever (hotioun allo pathos paschontos), he must consider the consequences that follow for this hypothesis in relation to itself (pros heauto) and in relation to each of the others

(pros hen hekaston tôn allôn), whether these others are taken individually, in groups (pleiô), or all together (xumpanta). Then he must do this, and in just the same way, for the others — hypothesizing both that they are and that they are not, and subject other qualifications, and discerning the consequences of these hypotheses both in relation to themselves and in relation to other others. It is only in this way, Parmenides asserts, that Socrates will be able to grasp the truth with authority (kuriôs diopsesthai to alêthes).

Central to this method of training is considering the consequences that follow from some hypothesis both “in relation to itself” (pros heauto) and “in relation to each of the others”

(pros hen hekaston tôn allôn), again whether taken individually, in groups (pleiô), or all together (xumpanta). Meinwald considers carefully the force of these qualifications, arguing that they mark a distinction between two kinds of predication.12 That is, in his transitional remarks and in the dialogue’s second part Parmenides distinguishes between,

12 The following tracks closely Meinwald (1992) 378-384.

1. A is B pros heauto (or, in relation to itself); and

2. A is B pros ta alla (or, in relation to the others)

The latter are our ordinary or everyday predications, where it is asserted that some subject exhibits or displays some character or quality. For example, “Solon is wise,”

“Wilbur is a cat,” or “The Good is intelligible.” The former are predications that reveal the structure of the subject’s nature. Importantly, they do not assert, as do predications pros ta alla, that some subject exhibits or displays some character or quality. This kind of predication is illustrated by way of the genus-species tree familiar from Linnaean classification. Meinwald reminds us that

a kind A appears either directly below or far below another kind B if what it is to be

an A is to be a B with a certain differentia (or series of differentiae) added. That is, the

natures of A’s and B’s are so related that being a B is part of what it is to be an A. In any

such case, B can be truly predicated of A (or of the A) in relation to itself, and so can A,

and so can any of the differentiae D. The idea here is that this kind of predication is

grounded in the structure of the nature in question: A’s nature is what it is to be an A —

that is, (a) B with ... with D, and it is in virtue of this that the predications hold. (1992,

379)

Examples of predications pros heauto include “the Pious is virtuous,” “Triangularity is three-sided,” and “the Pious is pious.” This distinction is important because sentences of the form “the A is B,” where the subject term names a Form, can be read as either predicating B of A pros heauto or predicating B of A pros ta alla. Equally important here is that these two different readings need not have the same truth value, and they always have different truth

conditions. Since these things are so, sensitivity to the context in which we find such sentences or statements is important if we are to determine their meaning.

Let us return now to Parmenides’s initial regress argument. We saw in its first stage that each member in some group of perceptible large things is large by participating in the Large itself. This explanation for why each perceptible large thing is large can be expressed as a predication pros ta alla: each perceptible large thing is large in relation to the Large itself.

We also saw in the second stage that the regress undermining Socrates’s belief in each

Form’s oneness depends in part on the claim that the Large itself is large. If this claim is read as a predication pros ta alla, then it means that the Large itself is large in relation to something other than itself. What is this “something other”? Presumably, it is a second Form of Largeness. But if this is so, and the second Form of Largeness is also large pros ta alla, then there must appear a third Form of Largeness, then a fourth, then a fifth, and so on ad infinitum. The mistake here, according to Meinwald, is treating the claim “the Large itself is large” in the same way as a claim asserting that some perceptible large thing is large — as a predication pros ta alla. Instead the claim “the Large itself is large” should be read as a predication pros heauto, as a claim that reveals something about the structure of the nature of the Large itself. If read in this way, then the Large itself cannot be grouped with the other large things; the Large itself and the other large things are not large in the same way. This, in turn, blocks the regress central to Parmenides’s initial regress argument.

While Meinwald’s distinction between, and interpretation of, predications pros heauto and predications pros ta alla does indeed stop the regress, I am not convinced that this is the correct interpretation of those qualifications central to Parmenides’s method of training.13

First, it is not clear to me why these two different ways in which something is predicated of a subject necessarily yield different sorts of predicates. Meinwald states that this is so, but

I cannot find in her monograph any explicit argument for this assertion. Perhaps it is a product of her reaction to literal readings of self-predicative statements, where the subject is a Form. Consider, for instance, the statement “Bravery is brave.” This, Meinwald writes,

“seems clearly false. It seems to be attributing a feature to Bravery that it could not have— we can hardly imagine it performing deeds of valor or bearing up under adversity” (1992,

365). It may also result from her illustration of predications pros heauto by way of genus- species trees. If, that is, predications pros heauto assert that something is predicated of a subject in virtue of its nature, where a subject’s nature is represented by its position in some genus-species tree, then it is plausible that what is predicated of this subject is only something pertaining to its position in this tree. Or as Meinwald sometimes writes, predications pros heauto “have a role Plato regarded as more fundamental [than predications pros ta alla]—namely, one of presenting the internal structures of the real natures” (1991,

71).

While this is a plausible inference, something more is needed to guarantee it. For there is a distinction between something being properly predicated of a subject in virtue of that subject’s nature and that what is predicated of a subject because of its nature can only be a

13 Additional concerns for Meinwald’s reading of these qualifications are in part the focus of Frances (1996), Pelletier and Zalta (2000), and Rickless (2007) 102-6.

predicate revealing its location in some genus-species tree. Meinwald herself seems to recognize this distinction when writing that predications pros heauto are “grounded in relations between natures” (1991, 67), “hold in virtue of a relation internal to the subject’s own nature” (1991, 70), and that the qualifications central to Parmenides’s method of training “mark a difference in the way in which B can be predicated of A” (1991, 70; italics in original), all of which concern the former but none of which by themselves justify inferring the latter. So, although I am inclined to agree with Meinwald that these qualifications specify how something is predicated of a subject, I remain unconvinced that they also influence or determine what is predicated of that subject—that something predicated pros heauto of a subject can only be a predicate revealing its location in some genus-species tree, and not the exhibition or display of some character or quality.

In addition, I contend that there is at least one reason for rejecting Meinwald’s interpretation of these qualifications. Above I wrote that, according to Meinwald, statements of the form “the A is B,” where the subject term names a Form, can be read as either predicating B of A pros heauto or predicating B of A pros ta alla. We have seen examples of each, but let me offer two more. Consider the statement “the Different has being,” where this is read as a predication pros ta alla. The complete statement read in this way is “the

Different has being in relation to Being.” The Different, that is, exists because of its relation to (read: through its participation in) something other than itself, namely Being. There is nothing problematic about this. Indeed, it is explicitly stated in the Sophist.14

14 The entirety of Soph. 254b10-257a12 is relevant here. But see especially 254d10-11, where both Motion and Rest are because Being mingles (mikton) with them. At 256a1 the Eleatic Stranger says that Motion exists because of its participation (metechein) in Being, and this is reaffirmed at 256d7-8. These particular conclusions are then said to hold for all Forms or Kinds (and so the Different) at 256c3-4.

What about the statement “the Different is different,” where this is also read as a predication pros ta alla? However we interpret these in-relation-to qualifications, we must do so in a way that allows for a reading whereby this is a genuine statement of self- instantiation. Consider the following argument from Soph. 255c12-e7, which demonstrates that the Different is a fifth Kind. Alternatively, that “the Different” and “Being” are not two names for one Kind (255c8-10). The argument proceeds in roughly this way: among “the things that are” (tôn ontôn) some are always spoken of (aei legesthai) themselves by themselves (auta kath’ hauta) and some in relation to others (ta ... pros alla). The Eleatic

Stranger observes that “difference” is always spoken of in relation to others. Why so?

Assume (for reductio) that Being and the Different are not almost entirely different

(pampolu diepheretên). That is, assume that the Different partakes (meteiche) in both classes

(amphoin ... toin eidoin), as does Being. What are “the classes” that the Eleatic Stranger refers to here? For the argument to go through, “the classes” must be these two ways of speaking of “the things that are” mentioned earlier: “themselves by themselves” and “in relation to others.” We are assuming, then, that just as “the things that are” are sometime spoken of as “being themselves by themselves,” and are sometimes spoken of as “being in relation to others,” so it is that “the things that are” are sometimes spoken of as “different themselves by themselves,” and are sometimes spoken of as “different in relation to others.”

But there is something odd that follows from this assumption. The Eleatic Stranger points out that if this is so, then there would be something (ti) of the others (tôn heterôn) that is other (heteron) but not in relation to another (ou pros heteron). Put differently that there is something that is different, and it is rightly spoken of as “different,” but not in relation to some other thing from which it is different. Rather this thing (whatever it is) is different by itself and not in relation to some other thing. But this is not found at all. As it is, he asserts,

we find that whatever is different is what it happens to be (sumbebêken ... einai) out of the necessity or compulsion (ex anagkês) of some other (heterou). Since the assumption that the

Different partakes in both classes just as does Being, where it is the class of auta kath’ hauta that is of interest, requires something to be found that is not found at all, it follows that the

Different does not partake of both classes. That is, “difference” is not spoken of itself by itself but always in relation to others. For this reason, then, the Different is indeed a fifth

Kind; “the Different” and “Being” are not two names for one Kind.

Concluding that the Different is indeed a fifth Kind is tantamount to concluding that the

Different is different (from Being).15 We must, I submit, interpret this statement as a genuine statement of self-instantiation. There is no other reading of it that follows from the argument constructed here between the Eleatic Stranger and Theaetetus.16 Presumably too is the

Different different in the same way that perceptible things (and other Kinds or Forms, come to that) are different — all of them exhibit the same character of difference. But this is not to say that the explanation for why the Different is different is the same as that explanation for why other Forms or perceptible things are different. It is also not to say that this same character of difference exhibited by the Different and other Forms, on the one hand, and perceptible things, on the other hand, is apprehended in the same way. More often than not I apprehend that each member in some group of perceptible things is different from the others through sensation — I simply see that this table is different from this chair, and these two

15 Consider too Soph. 254e2-255a2.

16 Thus, I disagree with Owen (1971) 255-8 who contends that this argument yields an identity statement. Instead, I am in agreement with Vlastos (1973) 337 n. 7 and n. 13 who notes that the argument demonstrates that “the Different is different (from Being).”

from my notepad and pen — whereas the Different was apprehended as different through reasoning (recall here Parmenides’s remark at 135d8-e3).

There is more to say about Meinwald’s reading of the Parmenides, and I will return to it in Chapter 3. For the moment, though, I set it aside, along with any response that engages with (SI).

F. One over many (OM)

I want to now consider (OM). Recall that it reads,

(OM) For any group of things exhibiting some quality in common (of the

appropriate sort), there is one Form that accounts for the exhibition of that

quality by each of the things in that group.

An answer to Parmenides’s initial regress argument that focuses on this assumption maintains that as formulated (OM) is too general — it does not distinguish between perceptible things, on the one hand, and Forms, on the other. An appropriately restricted

(OM) by this answer would read, “For any group of perceptible things exhibiting some quality (of the appropriate sort) in common, there is one Form that accounts for the exhibition of that quality by each of the perceptible things in that group.” By restricting

(OM) to only perceptible things, a step central to Parmenides’s initial regress argument is blocked.

This is admittedly an attractive answer. But it will not do. Consider that passage with which we are now familiar: Soph. 255c12-e7. Once the argument distinguishing the

Different from Being concludes, the Eleatic Stranger asserts that the Different “permeates

them all; for each one is different from the others, not by reason for its own nature, but because it partakes of the Form of the Different.” Here there is a group of things — Being,

Sameness, Difference, Motion, and Rest — that exhibit the quality of difference in common.

What accounts for the exhibition of this quality by each of the things in this group? Each member’s participation in one Form, the Different. This is a straightforward application of

(OM). Rather, it explains how that group is in fact a group that exhibits some quality in common. It is clear, I submit, that if the solution to Parmenides’s initial regress argument is restricting (OM) to only perceptible things, then we would not find this explanation for how these megista genê are different. But here it is. Restricting (OM), then, cannot be the correct way of preventing the argument’s regress.

F. Non-identity (NI)

If my arguments so far are sound, then our attention must turn to (NI). Recall that it reads,

(NI) No Form that accounts for the common quality exhibited by some group of

things is itself part of that group.

We saw above that this assumption determines when, say, the Large itself can fulfill a particular role: explaining why each member in some group of large things is large. (NI) asserts that the Large itself can fulfill this explanatory role only when it is not grouped with some set of large things that participate in it. But why? Why would grouping the Large itself with the other large things, which are large through their participation in the Large itself, preclude the Large itself from fulfilling this explanatory role?

The answer must in some way center on “grouping.” Let us, then, consider those ways in which the Large itself and the other large things could be grouped together. Assuming that

(SI) is partly constitutive of Plato’s position, then the Large itself is a large thing in the same way that the other large things are large — all of them exhibit the same quality. Given this assumption, the Large itself and the other large things could be grouped together simply because all of them are large things.

This is not the only way, though, in which the Large itself and the other large things could be grouped together. In addition to all of them exhibiting the same quality in common, both the Large itself and the other large things are large by participating in the same Form.

Here what groups all of them is, ultimately, their participation in the same object. Yet it seems that there is something more fundamental than this that could group the Large itself and the other large things. For to say that all large things are large through participation in the same Form does not say how each large thing participates in this Form. The last way in which the Large itself and the other large things could be grouped together specifies a type of participation: all of them participate in something other than themselves, namely, the one and the same Form by which all of them are large. So, there are three ways in which the

Large itself could find itself grouped with the other large things,

1. By exhibiting the same quality as all other large things;

2. By participating in the same Form as all other large things;

3. By being a large thing through participation in something other than itself, just as all other large things are large through participation in something other than themselves, where this “something other” is the same in every case.

The first way concerns the quality, the second way concerns the object, and the third way concerns the type of participation. Finally, let me state that these ways of grouping the

Large itself with the other large things are not mutually exclusive. For instance, if the Large itself and the other large things are grouped in the second way, then they are also grouped in the first way. But it is the second way that is the reason for their grouping, and the first way is merely a consequence of this.

Recall now the second stage of Parmenides’s argument, where Parmenides asks

Socrates, “Yet what about the Large itself and the other things that are large? If you regard all things the same way in your mind’s eye (ean hôsautôs tê psuchê epi panta idês), will not yet again one large thing make its appearance by which all those things necessarily appear large?” (132a5-7). Here Parmenides assumes not just that the Large itself exhibits the same quality as the other large things, which groups them in the first way. He also assumes that all of them are large by participating in the same Form, which groups them in the second way, and that each large thing participates in this same Form in the same way as any other large thing. Put differently, behind Parmenides’s questions is this inference: if the Large itself and the other large things are grouped in the first way, then they must also be grouped in the second way and the third way.

Why does Parmenides assume that if the Large itself and the other large things are grouped in the first way, then they must also be grouped in the second way and the third way? Answer: Parmenides understands that Socrates has no other available explanation for why the Large itself is large than that same type of explanation through which the other perceptible large things are large. Thus, if the Large itself and the other large things are grouped in the first way, then the Large itself along with the other large things can only be large through participation in the same Form. Here “participation” minimally amounts to participation in something other than themselves, where this “something other” is the same

in every case. But if this is the explanation for how the Large itself is large, then no longer can the Large itself explain why the other large things it is grouped with are large as it purported to do in the argument’s first stage. For the Large itself cannot be both “the same

Form” because of which all large things are large, as required by the second way of grouping, and “the something other,” as required by the third way of grouping. It is in this way, then, that from the above inference there is this requirement: “no Form that accounts for the common quality exhibited by some group of things is itself part of that group.” When the original (that is, the first) Form of Largeness is grouped by quality with the other large things, there is nothing to prevent its also being grouped by object and by type of participation with the other large things, a grouping that forces the Large itself to abandon its explanatory post. There now and must appear by (OM) another (that is, a second) Form of Largeness. But since by (SI) the second Form of Largeness is itself large, exhibiting the same quality as all other large things, it too can be grouped with the other large things that are large through their participation in it. Once this happens, though, it meets with the same fate as the first Form of Largeness. There then appears a third Form of Largeness, then a fourth, then a fifth, and so on ad infinitum.

Why does Socrates have “no other available explanation”? What prevents Socrates from, say, appealing to something we might call “self-participation” as the explanation for why the

Large itself is large? If such an appeal were made, then the Large itself and the other large things would be grouped in the first way and the second way, but not the third way. And notice that it is this last way of grouping the Large itself and the other large things that ultimately grounds (NI), which together with (SI) and (OM) generates the regress undermining Socrates’s belief that each Form in one.

My answer is that in the dialogue’s first part, the accounts of participation proposed by

Socrates are not compatible with “self-participation” as an explanation for how some Form is characterized by the very quality it constitutes. (More on this below.) However, I will argue in Chapter 4 that Plato himself is aware that this is an option, and that he endorses self-participation as the explanation for self-instantiation in the Sophist. Once again, it is my view that Plato uses this argument, along with the later Likeness regress (the subject of

Chapter 2), to encourage his reader to consider how and why some Forms self-instantiate.

Here is why Socrates cannot appeal to “self-participation.” This argument from

Parmenides is the third in a series of arguments, all of which presuppose a particular account of participation.17 We might call this “the Whole/Part account of participation.” By this account, participation is roughly this: either the whole Form, being one, is in each of its many participants (131a9-10). Or the Forms are divisible into parts, and any Form’s participants partake of a part, so that in each of them there is only a part of this Form

(131c6-9). Are either of these accounts compatible with some Form’s participating in itself?

First, the interpretation whereby the whole Form, being one, is in each of its many participants. Here the Large itself is, as a whole, in each of its participants and, as a whole, is also in itself. This is incoherent. For the container and that which is contained must be different things, not to mention that the Large itself would, as Parmenides points out, still be separate from itself and so not one (131b1-3).

17 This is confirmed at the outset of the third argument, where Socrates’s proposes that “each of the Forms is a thought (noêma), and occurs only in our souls. Then each of them might be one (hen) and no longer face the difficulties mentioned just now’ (132b4-8).

Second, the interpretation whereby the Forms are divisible into parts, and any Form’s participants partake of some part, so that in each of them there is only some part of this

Form. This interpretation is a bit more puzzling. By it the Large itself is divided into parts, and its parts are distributed among its participants. Given this, it would seem that, strictly speaking, there is no “the Large itself” for some part of the Large itself to be in, as other parts of the Large itself are in its other participants. At best, we can propose that some part of the Large itself will be in another part of the Large itself. The problem, though, is that that part is just that — it is a part of the Large itself, and not the Large itself. Thus, here too is self-participation precluded, not to mention that the Large itself is no longer one.

There is no help to be found in looking ahead in this dialogue to the account of participation that replaces this Whole/Part account of participation. The opening section of what I shall call “Parmenides’s Likeness Regress” (132d2-133a7) — which, again, is the subject of Chapter 2 — has Socrates propose to Parmenides that

These Forms stand as paradeigmata in nature (ta men eidê tauta hôsper

paradeigmata hestanai en tê phusei), and these others resemble (eoikenai) and are

likenesses (homoiômata) of them; and this participation for other things in the Forms

becomes nothing other than resembling (eikasthênai) them. (132d2-6)

By this account of participation, “self-participation” means some Form “resembles” or

“is modeled on” (eikasthênai) itself. The explanation, then, for how the Large itself is large is that the Large itself resembles or is modeled on itself. This will not do. For if the Large itself is large because it resembles or is modeled on itself, then the Large must already be large if resemblance or the-being-of-a-model is in fact possible. But if this is so, then the

resulting explanation is circular, and the Large’s largeness fails to be explained at all. So too for all other Forms.18

Given these reasons, among others, it should come as no surprise that Parmenides will later tell Socrates he has prematurely tried to define each one of the Forms before properly training himself (135c8-10), and that this has caused his difficulties. Since the Large itself and the other large things are grouped in the first way, and no alternative explanation is available to Socrates for why the Large itself is large, then so too must they be grouped in the second way and, more importantly, the third way. The Large itself, just as its perceptible participants, must be large by participation in the same Form. Moreover, the Large itself must participate in that same Form in the same way as its perceptible participants — participation in “something other” where this is the same in every case. So begins the argument’s regress, and so much the worse for Socrates.

It is not unreasonable in the light of this borderline-verbose analysis to favor rejecting

(SI) and reinterpreting statements of the form “the F is F.” After all, if the Large itself is does not exhibit the same quality as the other large things — if there is some other sense in which the Large itself is large — then it cannot be grouped even in the first way with the other large things. Yet I trust that this analysis reinforces that reinterpreting (SI) is not the correct line of response, as it does not touch the issue that is at the heart of this argument.

Grouping the Large itself with the other large things in the first way is not the problem. The problem is the argument’s treatment of the Large itself as something other than itself. Put differently, the problem is treating the Large itself as if it were a perceptible thing. But the

Large itself is not a perceptible thing; it is a Form, specifically the Form that is “that which

18 A similar point is made by Strang (1963) 157-8.

is large” (ho esti mega). It is different in kind from all perceptible things, and different in nature from all other Forms. Thus, whatever the explanation is for how the Large itself is large, it should not be the same type of explanation for how the other large things are large.

One last comment: recall that Parmenides’s argument is arguably generalizable to all

Forms. If this is so, then consider the substitution of “the Different” for “the Large itself.”

The argument’s regress is generated in the same way. But here the solution is not rejecting

(SI), so that the Different is not different. The solution is not precluding the Different from exhibiting the same character of difference as all other different things. Rather, the solution is distinguishing the explanation for how all other things are different from the explanation for how the Different is different. It is not the first way or the second way of grouping some

Form and its participants that is the problem here. It is the third way of grouping, which forces a treatment of some Form as though it were not a Form at all.

What does all of this mean for (NI)? Since it is supported by an inference that requires treatment of the Forms as something other than themselves — as perceptible things — I submit that it must be outright rejected. It is in this way that, I suggest, Plato is urging us, his reader, to respond to Parmenides’s initial regress argument.

E. Conclusion

I began with an overview of Parmenides’s initial regress argument, and then outlined three ways of preventing the regress. The dominant response is rejecting (SI) and reinterpreting statements of the form “the F is F.” I argued that this cannot be the case, as some Forms must self-instantiate. It will also not do to restrict the scope of (OM). The only

remaining option is (NI). I explored this option, ultimately concluding that this assumption must be rejected.

Along the way I have asserted that Plato knew how to meet this challenge, and that he is using this argument to encourage his readers to consider how and why some Forms self- instantiate. Evidence for this claim emerges over the remaining chapters, and I leave it to the reader to assess its truth or herself at the dissertation’s end. The next chapter focuses on

“Parmenides’s Likeness Regress” (132d1-133a7). The dominant response to this argument is similar to the one considered here — denying that the Forms “resemble” or are “like” their perceptible participants. I argue that this cannot be the case.

II. Parmenides’s Likeness Regress

A. Introduction

This chapter is concerned with a different criticism of the theory of Forms. Specifically,

Parmenides’s fifth criticism, or what I will call Parmenides’s “Likeness Regress.” The argument’s success turns on the Form of Likeness’s being characterized by the very quality it constitutes. There is less scholarly agreement on just how to prevent this argument’s regress. But a prominent line of response that goes back to at least the fifth-century CE

Neoplatonist Proclus denies that the Form of Likeness self-instantiates. So here, too, is it sometimes said that Plato should jettison this tenet from the theory of Forms — again, the assumption here is that Plato did not know how to prevent the regress — or that he is here signaling that this tenet is to be jettisoned — again, the assumption here is that he did know how to prevent the regress. Whichever is ultimately the case, it is sometimes maintained that the lesson to be learned from this argument is that the Forms no longer self-instantiate. And this, together with the dominant response to Parmenides’s initial regress argument, has been thought to “seal the fate” for self-instantiation as part of the theory of Forms.

Here I argue against Proclus’s line of response. Also, I consider and reject a line of response from Schofield (1996), which focuses on (OM) and the particular account of participation that Socrates proposes at the outset of the argument. The result, I claim, is that we must consider how the Form of Likeness is “like” — if there in an explanation for how this is the case that is at the same time different from the explanation for how its participants are “like.” I sketch my answer at the chapter’s end: the explanation for Likeness’s being

“like” is its participating in itself, as there is evidence in the Sophist that self-participation is

the explanation for self-instantiation.19 Consequently, I maintain that the lesson to be learned from this argument is that we should reject what I call the “No Explanation by Self-

Participation Assumption” (NES).

B. Parmenides’s Argument

Let us begin with Parmenides’s argument, which I divide into six sections for ease of reference. After Parmenides has shown that Socrates’s most recent proposal — that each

Form may be a thought (noêma) that exists only in our minds — is untenable (132b4-e12),20

Socrates then asserts that,

(1) These Forms stand as paradigms, as it were (hôsper), in nature, and the other things

resemble (eoikenai) and are likenesses (homoiômata) of them; and this participation

of other things in the Forms becomes nothing other than resembling (eikasthênai)

them.

(2) If, then, [Parmenides] said, something resembles (eoike) the Form, can that Form not

be like the resembling thing (tô eikasthenti), insofar as it has been made like

(aphômoiôthê) the Form? Or is there some way (mêchanê) in which the like is not

like its like? — No.

(3) And is it not a great necessity that the like participates (metechein) in one and the

same Form (tou autou eidous) as its like? — It must.

(4) But given that there is something such that by participating in it like things are like,

will that not be the Form itself (auto to eidos)? — Absolutely.

19 A full defense of these claims is found in Chapter IV.

20 All references are to the Parmenides unless I indicate otherwise.

(5) Then it is not possible for anything to be like the Form nor the Form like anything

else. Otherwise, then always alongside the Form will another Form appear, and if

that is like something, another again; and it will never cease that always a new Form

comes to be if the Form turns out to be like that which participates in it. — Very

true.

(6) Then it is not by likeness that other things participate in the Forms; it is necessary to

search for something else by which they participate. — So it seems. (132d2-133a7)

Socrates proposes in (1), and quite confidently (malista emoige kataphainetai hôde echein, 132d1-2), a new account of participation.21 The Forms stand as paradigms in nature, and the sensible things (horomena, 130a1) resemble and are like them. Given these preliminaries, Socrates asserts that participation just is these other things resembling the

Forms. Parmenides then in (2) – (4) puts a handful of questions to Socrates, after which he proceeds in (5) to undermine Socrates’s proposal by means of an infinite regress. The result in (6) is that “it is not by likeness that other things participate in the Forms” (133a5-6).

Consequently, “it is necessary to search for something else by which they participate”

(133a6).

How does Parmenides generate the regress in (5)? Answering this question begins with

(2). Here Parmenides puts two questions to Socrates. The collective force of these questions is this: because Socrates’s account of participation in (1) involves the notions of

21 The contrast between Socrates’s confidence here and the absence of such confidence at the end of the Whole/Part Dilemma (130e6-131e7) is striking. There Socrates says that, as it seems to him, it is not at all easy (eukolon … oudamôs) to determine just how perceptible things participate in the Forms. Proclus at in Prm. 906.31-907.18 attributes this change in Socrates’s attitude to Parmenides’s exercise of his own maieutic art, not unlike the older Socrates’s exercise of it on the young Theaetetus.

resemblance and likeness, is it not the case that the Form and its participants stand in a symmetrical relationship to each other? Socrates agrees that they do indeed — the participants resemble or are like the paradigm, and the paradigm resembles or is like its participants. This symmetrical relationship between the Form and its participants is necessary for generating the regress in (5).

Parmenides inquires in (3) whether Socrates thinks that if two things are “like” each other then they must participate in one and the same Form. This question aims to secure

Socrates’s assent to the “One Over Many Assumption” (OM), my preferred formulation of which is

(OM) For any group of things that exhibits some quality (of the appropriate sort) in

common, there is one Form that accounts for the exhibition of that quality by

each of the things in that group.22

Although Parmenides does indeed secure in (3) Socrates’s assent to (OM), some scholars attempt to deny this.23 Why so? Consider what follows in (4). Here Parmenides asks

Socrates, “But given that there is something such that by participating in it like things are like, will that not be the Form itself?” The question appears redundant, as it seems to secure, albeit in slightly different language, nothing more than Socrates’s assent to (OM). But this is just what Parmenides does in (3)! Now redundancy itself is not necessarily a problem.

However, the particle de at 132e3 suggests that Parmenides is introducing something new in

22 The qualification is required in the light of Socrates’s earlier uncertainty concerning the extent of the Forms (130b2-e5).

23 For instance, Owen (1953) and Spellman (1983). The following is a summation with additions of Schofield (1996) 59-66.

(4). Scholars that interpret Parmenides’s questioning in this way consequently propose or outright adopt an emendation to the text in (3): the excision of eidous at 132e1.24 The result is that Parmenides asks Socrates, “And is it not a great necessity that the like shares

(metechein) in one and the same as its like?” The advantage is that Parmenides now introduces something new in (4). Parmenides asks Socrates in (3) whether, if two things are

“like” each other, must not they be “like” each other by sharing in some common quality?

Once Socrates assents to this, then in (4) Parmenides asks Socrates whether, if two things are “like” each other by sharing in some common quality, then must they not participate in one and the same Form? Socrates replies, “Absolutely.” Parmenides now secures Socrates’s assent to (OM) in two stages.

There are two further consequences of this emendation. The first is a reformulation of

(OM). Parmenides’s questions in (3) and (4) indicate that any two (or more) things that share some quality in common not only participate in one and the same Form, which explains their exhibition of that quality in common. These two things are also made “like” by participation in that same Form; they become qualified in not one but two ways. As such,

(OM) should now be formulated in this way (the changes are underlined),

24 Here is the Greek text: Τὸ δὲ ὅµοιον τῷ ὁµοίῳ ἆρ᾽ οὐ µεγάλη ἀναγκη ἑνὸς τοῦ αὐτοῦ εἴδους µετέχειν; (132d12-132e1). The emendation was first proposed by Jackson (1882) 291 n. 1. It has been widely adopted, including by Burnet in the Oxford Classical Text and Diès in the Budé edition. However, it is not universally adopted by those who find a redundancy in Parmenides’s questioning. Some, for instance Cherniss (1957) 253 n. 114, retain eidous but translate it in a neutral way as, say, “character.” But as Schofield (1996) 63 n. 22 rightly points out, “in a context such as Parmenides 129-35 where εἴδη as Form are the principal topics, and where every other instance of εἴδος means ‘Form,’ Cherniss’s proposal to take it as ‘character’ at this point is simply bizarre.” We shall see below that a similar point concerning metechein holds for those who would accept Jackson’s proposed emendation.

(OM*) For any group of things that exhibits some quality (of the appropriate sort) in

common, and because of which this group of things is also “like,” there is

one Form that accounts for the exhibition of these qualities by each of the

things in that group.

Second, it is now the case that participation in any Form results in two (or more) things being “like” each other. For example, if two paintings participate in the Beautiful, their participation in the Beautiful explains both why each painting is beautiful and why each painting is “like” the other.

While I do not deny that Parmenides introduces something new in (4), I do contend that this is the wrong way of securing his introduction of something new. The proposed emendation and its consequences should be rejected. I confine myself to two points, and start with (3). Even with the excision of eidous from Parmenides’s question, still present is the infinitive metechein. The verb metechô is one of Plato’s preferred terms for the participation relation between Forms and other things. With the excision of eidous, however, we cannot understand metechein here in this familiar and technical way. As Schofield writes, the emendation requires metechein “to function as a metaphysically unloaded word signifying ‘have in common’” (1996, 63). Why is this problematic? First, notice that in (1)

— only half a dozen lines prior — Socrates uses methexis, a cognate of metechô, to pick out just that participation relation between Forms and other things. Second, every instance of metechô up to this point, and beginning with Socrates’s introduction of the Forms at 128e7, picks out this same relation of participation between the Forms and other things.25 Third, the target of this particular regress argument is nothing other than Socrates’s new account of

25 See 129a9, b4, b7, b8, d1, d2; 130b4; 131c7, c8; 132a12, c10.

participation in (1) between Forms and other things. It is simply implausible, then, that metechein should be understood in (3) as “have in common.”

In addition, it is quite clear from what both Socrates and Parmenides say in this dialogue’s first part that there is just one Form that makes two (or more) things “like” each other. Consider the following passages,

1. 128e9-129a7: here Socrates asks Zeno, “do you not believe that there is a Form of

Likeness itself by itself, and another one that is opposite this, which is Unlikeness;

and that you and I, and all things that we call ‘many’ partake of (metalambanein)

these two? And that those partaking of Likeness become like, in the manner and to

the extent that they participate, and those partaking in Unlikeness become unlike,

and those partaking of both become both?”

2. 130e6-131a4: here Parmenides inquires, “tell me [Socrates]: does it seem to you, as

you say, that there are certain Forms, and that these other things partaking in

(metalambanonta) them are named from them, for instance those partaking in

Likeness become like, those partaking in Largeness become large, and those

partaking in Beauty and Justice become just and beautiful? — Certainly.”

Both passages are explicit that the explanation for two (or more) things being “like” is their participation in the Form of Likeness. For these reasons, we should reject the excision of eidous at 132e1, (OM*), and the contention that participation in any Form can make two

(or more) things “like” each other.

If it is not denied that Parmenides secures in (3) — in a single step — Socrates’s assent to (OM), then what is the something new that he introduces in (4)? Let us start a bit further

back to see it.26 According to Socrates in (1), participation just is things resembling the

Forms. Then in (2) Parmenides points out that insofar as a Form’s participants resemble that

Form, both the Form and its participants are “like” each other. After this he establishes in (3) that if two things are “like” each other, then they must participate in one and the same Form.

Which Form? It is an answer to this question that is provided in (4) — that by participation in which like things are “like” is nothing other than the Form itself, the Form of Likeness, just as we saw in the passages cited above. I contend that this is confirmed by the phrase auto to eidos in (4). This phrase refers to the Form of Likeness because auto picks out homoia in the previous clause.

In addition to (OM) and Parmenides specification that it is by participation in Likeness that like things are “like,” two more assumptions are required for generating the regress in

(5). One of these assumptions we have seen already. It was introduced and secured by

Parmenides in (2), and I shall call it the “Symmetry Assumption” (SA),

(SA) The paradigm and its copies are “like” each other.

The other is an assumption that precludes “self-participation” as the explanation for some Form’s being characterized by the very quality that it constitutes. It will become clear below that if the Form of Likeness, for instance, could explain its being “like” something else by participating in itself, then Parmenides would be unable to generate the regress in

(5). But there is a more important reason for excluding self-participation. Given the account of participation in (1), “self-participation” here means that some Form is characterized by

26 The interpretation that follows was originally proposed in Schofield (1996). It has since become the dominant interpretation in the literature. See Gill (1996) 42-5, Allen (1997) 179-93, Rickless (2007) 80-5, and Gill (2012) 39-41, among others.

the very quality it constitutes because it resembles or “is modeled on” (eikasthênai) itself.

For the sake of illustrating this point consider briefly the Beautiful, which is beautiful (Phd.

100c4-6). If the explanation of the Beautiful’s beauty is that it resembles or is modeled on itself, then the Beautiful must already be beautiful if resemblance or the-being-of-a-model is in fact possible. But if this is so, then the resulting explanation is circular, and the

Beautiful’s beauty fails to be explained at all.27 I will call this assumption, then, the “No

Explanation by Self-Participation Assumption” (NES),

(NES) No Form’s being characterized by the very quality is constitutes is explained

by “self-participation.”

Recognition of this point constitutes an important initial step in my argument, so let us stay with it for a moment. (NES) is a consequence of Socrates’s proposal in (1), as the above argument shows. There is nothing problematic about either of them, unless there is evidence for self-participation as the explanation for some Form’s being characterized by the quality is constitutes. I contend that there is such evidence in the Sophist, and I sketch this evidence at the chapter’s close.28 I will also suggest that, because there is evidence that self- participation is the explanation for self-instantiation, Plato ultimately abandons the proposed account of participation in (1) following the Parmenides.

For now, here is how the regress unfolds in (5). Let us take some beautiful thing, say,

Sekito Kisen’s eighth century CE poem Sandôkai. The explanation for its beauty, by

Socrates’s account of participation in (1), is the poem’s resemblance or likeness of the

27 A similar point is made by Strang (1963) 157-8.

28 Once more, a full discussion of the issue of self-participation is found in Chapter IV.

Beautiful. Although this latter is the paradigm and the former a copy, by (SA) both are

“like” each other. Since this is so, then by (OM) both the poem and the Beautiful must participate in one and the same Form. This “one and the same Form,” given Socrates’s and

Parmenides’s remarks from earlier in the dialogue, is none other than the Form of Likeness.

Recall now that by Socrates’s account in (1), participation just is other things resembling the

Form. So, to say that Kisen’s poem and the Beautiful participate in the Form of Likeness is nothing but saying that these copies resemble the Form of Likeness. Now by (SA) Kisen’s poem, the Beautiful, and the Form of Likeness, though copies and paradigm respectively, are “like” each other. Since this is so, then by (OM) all must participate in one and the same

Form. However, this “one and the same Form” cannot be the original Form of Likeness. It must be another (that is, a second) Form of Likeness. Why so? Because (NES) precludes self-participation as an explanation for the original Form of Likeness’s being “like.” It is this second Form of Likeness that now accounts for the “likeness” common to Kisen’s poem, the

Beautiful, and the original Form of Likeness. But by Socrates’s account Kisen’s poem, the

Beautiful, and the original Form of Likeness’s participating in the second Form of Likeness just is their resembling this second Form of Likeness. By (SA) Kisen’s poem, the Beautiful, the original Form of Likeness, and the second Form of Likeness, though copies and paradigm respectively, are “like” each other. Since this is so, then by (OM) all must participate in one and the same Form. However, this “one and the same Form” cannot be the second Form of Likeness. It must be another (that is, a third) Form of Likeness. Why so?

Because just as (NES) precludes self-participation as an explanation for the original Form of

Likeness’s being “like,” so too does it preclude this explanation for the second Form of

Likeness’s being “like.” It is this third Form of Likeness that now accounts for the

“likeness” common to Kisen’s poem, the Beautiful, the original Form of Likeness, and the

second Form of Likeness. This line of reasoning is, unfortunately for Socrates, repeatable indefinitely. Consequently, his proposed account of participation in (1) must be set aside.

For this regress demonstrates that there is no paradigm of likeness, no Form capable of fulfilling the explanatory role central to this account of participation. As Parmenides says,

“it is not by likeness that other things participate in the Forms; it is necessary to search for something else by which they participate” (133a5-6).

C. Possible lines of response

We turn now to possible ways of preventing the regress generated in (5). What are our options here? We might attempt to deny (SA), arguing that “likeness” is not always a symmetrical relation. This strategy goes back at least to Proclus (in Prm. 912.19-38), and I shall consider in the next section.29 Another possibility is restricting Socrates’s account of participation in (1) and (OM), so that they do not apply to the quality of likeness.30 This latter possibility, pursued by Schofield (1996), effectively eliminates the Form of Likeness from Socrates’s position (or if you prefer Plato’s position). I consider this possibility below in Section E. I will reject both of these lines of response. It is my position that we should focus on (NES), and I discuss this possibility below in Section F.

29 This strategy has found some favor in recent times too. See for instance Bestor (1980), Lee (1966), and Lee (1973). For a convincing response to these articles deployment of this strategy, see Schofield (1996) 67-8.

30 Below I will comment briefly on why Socrates’s account of participation and (OM) must be taken together.

D. Proclus

At the outset, we must address an important question. Above I argued that Parmenides in

(5) generates an infinite regress of Forms of Likeness. Does Proclus also interpret the argument in this way? The best evidence that I can find that he does is at in Prm. 915.24-

916.11, in a discussion concerning “unlikeness.” Here Proclus entertains this question: must one describe each Form itself as “like” or “unlike” the things that have come into being in accordance with it? He writes that, to answer this question, we must first get clear on the term “unlike.” For this term has two distinct senses. One sense of unlike means “that which participates in Unlikeness.”31 Another sense of unlike means the contradictory of “like,” which we might prefer to render as “not-like” or “neither like nor unlike” since, strictly speaking, “like” and “unlike” are not contradictory opposites. With this distinction in hand

Proclus proceeds with its application to the present question. He writes that the contradictory

“not-like” or “neither like nor unlike” is proper to the Forms. As we shall see below, Proclus maintains that the Forms are “not-like” or “neither like nor unlike” their participants, although these latter are likened to them. But the other sense of “unlike” — that which signals participation in the Form of Unlikeness — is not proper to the Forms. Why not? He writes,32

… for in that case [if the sense of “unlike” that signals participation in the Form of

Unlikeness were proper to the Forms] we would be in the same position as we were in

the case of Likeness, and the argument would be liable to an infinite regress. We will

31 Recall here Socrates’s own remarks at 129a1-b1, and compare Parmenides’s recapitulation at 130e6-131a3.

32 Here and throughout, unless otherwise indicated, I follow the translation of Morrow and Dillon (1987). For the Greek text, I consulted the edition of Steel (2008).

then be inquiring about Unlikeness also, whether it is “like” or “unlike” those things that

participate in it, and if it is “like,” then there will in turn be a Likeness prior to both; if it

is “unlike,” and is so in such a way as not to be according to the essence of Unlikeness,

then an Unlikeness prior to them, and this also involves an infinite regress.” (in Prm.

916.4-9; the translation is modified slightly, and with my emphasis)

From these considerations Proclus concludes that one may describe each Form itself as

“unlike” the things that have come into being in accordance with it, but only if by this it is meant that the Forms are “not-like” their participants.

Set aside for the moment whether there is a coherent sense in which the Forms are “not- like” their participants even though these latter are likened to them. Proclus’s line of reasoning against the sense of “unlike” that signals participation in Unlikeness as proper to the Forms strongly suggests that he too considers this second regress argument to turn on a regress of Likenesses. For notice that he writes both of a Likeness prior to both like things, one of which is the original Form of Likeness, and of an Unlikeness prior to both unlike things, one of which is the original Form of Unlikeness. And the former is just what I argued

Parmenides generates in (5).

Let us turn now to Proclus’s proposal for preventing Parmenides’s regress. Proclus maintains that even if the other things are “like” that Form in which they participate, it is not necessary that this relationship is reciprocal (antistrephein) and the Form is “like” its participants (in Prm. 912.16). Put differently, the Forms are “not-like” their participants even though these latter are likened to them. He is well aware that a reciprocal or symmetrical relationship between the Forms and the other things is necessary for generating the regress in (5). However, Proclus maintains that asserting that the Forms and their

participants stand in a symmetrical relationship to each other ignores a certain aspect of the

Forms, what he calls “the primal and universal causality of the paradigm” (tên prôtourgon aitian tou paradeigmatos kai holikên, in Prm. 912.13-4). Once Socrates appreciates the paradigm’s particular sort of causality, this introduces an asymmetry between the Form and its participants. Consequently, Socrates will reject (SA), preventing the regress in (5), and thereby preserve his proposed account of participation in (1).

What is this sense in which the Form is “not-like” its participants even though these latter are likened to it? Proclus writes,

… Socrates should have replied that “like” has two senses, one the likeness of two

coordinate entities (to men suzugos hôs homoiô homoion), the other the likeness which

involves subordination to an archetype (to de hôs hupheimenon pros archetupon

homoion), and the one is to be seen as consisting in the identity (tautotêti) of some one

principle (logou), while the other involves not only identity but at the same time

otherness (to heteron), whenever something is “like” as having the same form (to tauton

eidos) derived from the other, but not along with (met’) it. (in Prm. 912.24-29; italics in

the original translation, and modified slightly)

The distinction drawn here is this: there is a sense of likeness applicable to two coordinate entities, consisting in the identity of some one principle; and there is another sense of likeness involving subordination to an archetype that, though in part includes the identity of some one principle, also incorporates an otherness. On this latter sense of likeness, the identity of some subordinate entity is derived from the other — that is, the archetype — but not along with this other.

Understanding this distinction starts by recalling something introduced above. Proclus distinguishes two senses of unlike at in Prm. 916.4-9, and maintains that the sense of unlikeness that signals participation in the Form of Unlikeness is not proper to the Forms.

For if it were, then there would be an infinite regress of Forms of Unlikeness. Yet the Form of Unlikeness is not the only Form in which no other Form participates. It is also the case that no Form participates in the Form of Likeness. The reason is the same: if other Forms participated in the Form of Likeness, then there would be an infinite regress of Forms of

Likeness, just as we saw Parmenides generate in (5). It is a consequence of this that no Form is “like”; neither is it “like” its participants nor any other Form. This is confirmed by

Proclus’s assertion that the sense of unlikeness that is proper to the Forms is contradictory of

“like,” which we might prefer to render as “neither like nor unlike.”

While this distinction between senses of likeness does result in the Forms’ being not

“like” their participants, this is not the end of Proclus’s response. For Proclus maintains that a symmetrical relationship between the Forms and their participants neglects “the primal and universal causality of the paradigm” (in Prm. 912.13-4). It is this that Proclus’s distinction is meant to illuminate, and it does so by dividing the sense of likeness that is proper only to the

Forms’ participants, called here “coordinate entities.” The participants are “like” in the sense that they are qualified in the same way, that they share an identical principle. For example,

Kisen’s poem and Matisse’s “the Dessert” are “like” each other with respect to their beauty, they share the identical principle of beauty. But Kisen’s poem and Matisse’s painting are also “like” in another way. This sense of likeness involves subordination to an archetype, namely the Beautiful. It is by participation in the Beautiful that Kisen’s poem and Matisse’s painting possess the identical principle of beauty; they derive it from the Beautiful, which also shares this principle with them. Yet the Beautiful is not itself a coordinate entity — it is

not coordinate with either Kisen’s poem, Matisse’s painting, or anything else that participates in it — because the Beautiful and its participants occupy different explanatory levels. The participants’ being beautiful, their possession of this principle, is entirely dependent on their participation in the Beautiful itself. The Beautiful’s beauty, however, is not dependent on its participants. Its possession of this same principle is explained in a way different from that of its participants.33 Thus the Beautiful’s participants derive their beauty from the Beautiful, but they do not derive it, as Proclus puts it, along with the Beautiful. The

Beautiful does not come to occupy the same explanatory level as its participants because the causality is unidirectional and indeed universal. I submit that this distinction of two explanatory levels, grounded in the Forms’ unidirectional and universal causation, is precisely what Proclus’s means by “the primal and universal causality of the paradigm” (in

Prm. 912.13-4). The Beautiful, continuing with our example, is the cause of the beauty of all things.

With this we return to (2), where Parmenides introduces and secures Socrates’s assent to

(SA). For the sake of convenience here is the text,

If, then, [Parmenides] said, something resembles (eoike) the Form, can that Form not

be like the resembling thing (tô eikasthenti), insofar as it has been made like

(aphômoiôthê) the Form? Or is there some way (mêchanê) in which the like is not like

its like?—No. (132d7-11)

33 Recall here the rather striking remark by Proclus at in Prm. 916.8-9. If the sense of unlikeness proper to the Form is “participates in the Form of Unlikeness,” then we will inquire about Unlikeness itself and whether it is like or unlike its participants. He continues, “if [Unlikeness] is unlike, and is so in such a way as not to be according to the essence of Unlikeness (houtôs hôs ou kata metousian tês anomoiotêtos), then an Unlikeness prior to them, and this also involves an infinite regress” (my emphasis).

We are now positioned to see why, according to Proclus, the symmetrical relationship between some Form and its participants asserted here does not in fact hold between them.

The relationship between the Forms and their participants is not one of mere resemblance, as

Parmenides’s question suggests. As A. E. Taylor observes, “it is in fact a relation of resemblance+derivation, and this relation is not symmetrical” (1908, 358).34 Consequently,

(SA) is false, and its rejection prevents the regress in (5). This, in turn, saves Socrates’s account of participation in (1).

While some champion Proclus’s response, others remain unconvinced by it. Owen, for instance, maintains that the response is fallacious, writing “it argu[es] as though, because the relation between copy and original is not simply resemblance, it does not include resemblance; for if it is included Parmenides’ regress follows at once” (1953, 83 n. 3, original emphasis). Schofield puts the point differently, “even if the original-copy relation doesn’t reduce to the symmetrical likeness relation, does it not entail it? If it does … then, for all the objector has shown, the argument is not only valid but reveals very effectively an unacceptable consequence of the original-copy model” (1996, 66-7, original emphasis).

I shall not enter into this debate here. For the success or failure of my own argument does not turn on this issue. If Proclus’s introduction of an asymmetry between the Forms and their participants is defensible, it must still be rejected. The reason is straightforward:

Proclus’s response is incompatible with Forms participating in other Forms. On the other hand, if it is not defensible, then my argument is further confirmation that this line of response should be rejected.

34 See also Cornford (1939) 92-5.

We saw above that the Forms are not “like” (nor “unlike” for that matter) their participants because they do not participate in the Form of Likeness (or Unlikeness), and that this is an important step in Proclus’s contention that there is an asymmetry between the

Forms and their participants. Yet the participants are nevertheless likened to the Forms.

Proclus explains this latter in response to the question, “Does the Form of Man create only the man of this realm, or does it also make him like to itself?” (in Prm. 916.13-14). His answer (in Prm. 916.15-28) begins with a statement of the two options: either the Form of

Man gives the men of this realm only their substance (tên ousian) or it gives the men of this realm their substance and assimilation (aphomoiôsin) to itself. However, both options appear problematic. Proclus notes that by Socrates’s account in (1), participation in some Form just is some thing’s resembling or being likened to that Form. If the Form of Man gives the men of this realm only their substance, then it does not make them an image of itself, since it does not liken them to itself. Consequently, the men of this realm do not participate in Man at all. On the other hand, if the Form of Man gives the men of this realm their substance and assimilates them to itself, Proclus asks, What role is left for the Form of Likeness? It seems that there is no need for this Form. He contends that the solution is recognizing that the

Forms operate in concert with each other, fulfilling different roles. Although their activities are artificially distinguishable, in actuality they are unified. Proclus explains that the Form of Man gives to the men of this realm their substance and through Likeness, by possessing this substance, the men of this realm are likened to the Form of Man. Likeness creates the men of this realm. But not qua man, as Proclus puts it.

This explanation undoubtedly raises many questions. For our purposes, though, the important item is this: according to Proclus, anything that participates in some Form in fact participates in that Form and in the Form of Likeness. Participation in the Form of Likeness

is now necessary for participation in any Form at all, as Likeness has the role of assimilating or likening participants to whichever Form has imparted its substance. For example, the explanation for Kisen’s poem being beautiful is the Beautiful’s imparting its substance to

Kisen’s poem, and Likeness likening Kisen’s poem to the Beautiful. This refinement to the resemblance account of participation is not problematic insofar as Forms do not participate in other Forms. But if Forms do participate in other Forms, then we must reject Proclus’s refinement. The reasoning is straightforward: since no Form participates in the Form of

Likeness, no Form can resemble or be likened to the other Form in which it participates. But without resembling or being likened to the other Form in which some Form participates, that

Form does not in fact participate in the other Form.

When we look to the Sophist, it is clear that Forms participate in other Forms. The section on the Great Kinds (Soph. 254b8-257a12) states that Change (kinêsis) and Rest

(staseôs) both mix with (mikton) Being (on), since they both are (Soph. 254d10-11); Being,

Change, Rest, Sameness, and Difference all participate in (metechein) Difference, and for that reason are different from each other (Soph. 255d3-6); Change is because of its participation in (metechein) Being (Soph. 256a1); Change is the same as itself because it partakes of (metechein) Sameness (tauton) (Soph. 256a7-8); and so on. Recall that Proclus’s response to Parmenides’s argument requires that no Form participates in the Form of

Likeness. At the same time, though, he turns participation in the Form of Likeness into a necessary condition for participation in any Form at all. Consequently, this refined resemblance account of participation is rendered incompatible with Forms participating in other Forms. For this reason, I submit that Proclus’s line of response must be rejected. This is not the lesson to be learned from Parmenides’s argument.

E. Schofield

Let us see now Schofield’s preferred line of response. Schofield maintains that we ought to question whether Socrates’s account of participation in (1) applies in the case of likes. I mentioned above that restricting Socrates’s account of participation must result in a similar restriction on (OM).35 Why so? While I provided above a formulation of (OM), I have not yet provided such a formulation of Socrates’s account of participation. Here is such a formulation,

(P) Anything exhibiting some quality (of the appropriate sort) does so in virtue of

being modeled on the Form corresponding to that quality.36

As I understand it, (P), though closely connected with (OM), is nonetheless distinct from

(OM). Recall that, as I argued in the previous chapter, (OM) explains how each member in some group of things that exhibits some quality in common is in fact a group of things exhibiting this quality in common. It does so by asserting that each member in this group of things participates in one and the same Form. It is participation in this Form that accounts for how this group of things is in fact that group of things. (P) fills out this explanation by specifying just what “participation” is; within the confines of this argument, “participation” is nothing but each member in some group of things being modeled on the Form that corresponds to that quality exhibited in common. Thus, a restriction on the qualities to which the participation-relation applies requires a similar restriction on which groups of

35 Note that this restriction on (OM) is different from that restriction discussed in the previous chapter. There I considered whether (OM) can be restricted to perceptible things, ultimately arguing against this.

36 Remember that this parenthetical reflects Socrates’s earlier uncertainty concerning the extent of the Forms (130b2-e5).

things can be explained by (OM) as in fact a group of things that exhibits some quality in common.

What, then, is the case for restricting Socrates’s account of participation and (OM), so that neither applies in the case of likes? It begins by noticing the attention given to

“likeness” in this dialogue’s first part. Zeno’s paradox, which ushers in the introduction of the Forms by Socrates and their subsequent examination by Parmenides, turns precisely on it

(127e1-10); Socrates’s response to Zeno’s paradox begins with the Form of Likeness

(128e8-129b6); and Parmenides mentions it again in his summation of Socrates’s position

(130e6-131a3; compare 130b2-7). It is not surprising, then, that later in dialogue Parmenides would return to it if presented with the opportunity. As Schofield writes, “It is as though

Parmenides is made to say: ‘Platonism propounds a thesis about likeness which (as it claims) shows Zeno’s paradox about like and unlike to be trivial — but, if the thesis is conjoined with the original-copy theory of participation, it wrecks the Platonism of which both are elements.’” (1996, 69).

It is not just this dialogue’s first part, though, that gives “likeness” due attention. The dialogue’s second part has much of interest too, as consequences concerning the One and its relation to the others with respect to likeness (and vice versa) are found in all eight deductions. What are we to learn from the lengthy exercise concerning this particular quality? Schofield starts by drawing our attention to Parmenides’s statement in the first deduction that to tauton pou peponthos homoion, “what is qualified in the same way is

‘like’” (139e8-9). This phrase occurs again in the second deduction at 148a4-5. He asserts, noting his agreement with other commentators, that this phrase expresses an analysis of

likeness (1996, 70); “likeness” just is “that which is qualified in the same way.”37 Moreover,

Schofield contends that this is an analysis “that completely avoids any reference to the metaphysics of Forms and participation, or, indeed, to an ontology of any sort” (1996, 71).

On this last point, he invites us to consider the use that this analysis is put to in the third deduction. Here Parmenides demonstrates that the others are both like and unlike themselves and each other.38 The argument, which runs from 158e1-159b2, is roughly this: the others are all by their own nature unlimited, and in this respect they are all qualified in the same way. But at the same time the others all partake (metechei) of limitation,39 and in this respect too they are all qualified in the same way. Consequently, it is with respect to either of these qualities that the others are “like” themselves and each other. However, since limitlessness and limitedness are opposites, with regard to both qualities together the others are “unlike” themselves and each other. Thus, the others are both like and unlike themselves and each other. The important phrases here are tauton peponthota an eiê tautê at 158e2-4 and tautê

37 Similar analyses for other qualities are found in the deductions. Consider for instance 140b8-c2, in the first deduction, where “equality” is described as that which “has the same measures as that to which it is equal”; “largeness” is described as that which “has more measures than the things which are smaller”; and “smallness” is described as that which “has fewer measures than the things which are larger.” Note, though, the alternative descriptions in the second deduction at 150c8-e6 where consideration of measures is replaced with “the capacity to exceed or be exceeded” (dunamin tên tou huperechein kai huperechesthai). The result is that here “equality” is “that which neither exceeds nor is exceeded”; “largeness” is “the capacity of exceeding”; and “smallness” is “the capacity of being exceeded.”

38 The last use of this analysis occurs in the seventh deduction at 165c8-d1. The eighth deduction demonstrates that the others, if the One does not exist, are neither like nor unlike in a different way.

39 This is the single occurrence in the argument of any participation language. But it does not affect Schofield’s point. For it is by partaking in the One that, in a way, the others become limited with respect to each other (158d3-6). Schofield’s point here, again, is that it is not by participating in Likeness that like things become like. I return to this below.

pant’ an eiê tauton peponthota at 158e4-5, both of which are loosely rendered in this summation as “in this respect (too) they are qualified in the same way.” Since, as is stated in the first deduction and the second deduction, what is qualified in the same way is “like,” the others all being qualified in either of the ways just mentioned is sufficient by itself to yield here part of Parmenides’s desired conclusion — that the others are all “like” themselves and each other.

The argument arguably does not reference Forms (though we shall return to this point below). In addition, Schofield highlights Parmenides’s use of the verbal forms peponthei and peponthos here and elsewhere in the dialogue’s second part. As I understand the significance of this latter, it is that these verbal forms do not bring with them the same metaphysical baggage as the language of methexis. Indeed, Schofield advances the stronger claim that at least in the case of likeness and unlikeness these verbal forms replace the language of methexis. Parmenides’s dialectical display demonstrates in part, he writes, “that we can handle claims that something is like or unlike perfectly adequately by taking them simply as assertions to the effect that something is qualified in the same or a different way”

(1996, 71).

Finally, Schofield directs us to an argument at 159e2-160a3 from the fourth deduction. It proceeds in roughly this way: if the others were like or unlike, or had likeness and unlikeness in themselves, then they would have two Forms (duo ... eidê) opposite each other in themselves. But it is impossible for things which do not participate (metechoi) even in one thing to participate (metechein) in two. Therefore, the others are neither like nor unlike, nor both. For if they were like or unlike, then they would participate in one or other of the Forms

(henos an tou heterou eidous metechoi), and if both then in the two opposite Forms (douin toin enantion). But these options appeared impossible.

Here Parmenides establishes a result concerning the others that is in outright contradiction with the above argument from the third deduction: that the others are neither like or unlike the One, nor is there likeness and unlikeness in them. According to Schofield,

Parmenides is able to derive this result concerning the others precisely because he uses the language of methexis and not, as in the above argument, the language of pathos. Still, why should Parmenides do this? The answer is “to underline in red ink the contrast between the two stories” (1996, 71). The language of pathos allows us to make sense of talk about likeness and unlikeness, while the language of methexis leads us into confusion.

Although this is just a sampling of passages from the dialogue, Schofield deems them sufficient for establishing his conclusion. He writes,

I submit that the reader of part II of the dialogue will see reason to reject [the

assumption that Socrates’s account of participation in (1) applies in the case of

likes]. He has come to appreciate that to understand talk about items being like each

other is merely to grasp that they are qualified in the same way, i.e. have the same

predicate true of them. To put it differently, what the reader has effectively

recognized is that like is a second-order predicate: “is like” means “shares the same

first-order predicate,” not “participates in the Form Likeness.” (1996, 72)

Put differently, the reader of this dialogue’s second part will reformulate Socrates’s proposed account of participation in (1) as, “any two things sharing the same first-order

predicate F do so in virtue of being modelled on an original, F-ness” (1996, 73).40 And as I argued above, this necessitates a restriction on (OM). This latter should now read, “For any group of things that exhibits some first-order predicate in common, there is one Form that accounts for the exhibition of that first-order predicate by each of the things in that group.”41

These restrictions, in turn, prevent the regress from being generated in (5).

Is this the lesson to be learned from Parmenides’s Likeness Regress? I believe not. What follows, though, is by no means a decisive critique. This is in part because, as we shall see,

Schofield himself is aware of this line’s challenges. It has far reaching implications, and is bound-up with larger questions concerning the development of Plato’s thought into the late dialogues. The other reason concerns space. I cannot discuss here all those arguments that deal with likeness and unlikeness in this dialogue’s second part, much less those that focus on closely connected qualities (notably, sameness and difference). Moreover, it is not possible for me here to present and defend a general interpretation of this dialogue’s second part.42 These things being so I confine myself to those passages mentioned above, in addition to a more general criticism.

Recall that, according to Schofield, we learn from the dialogue’s second part “that we can handle claims that something is like or unlike perfectly adequately by taking them

40 The changes with the original formulation are underlined. Note that Schofield’s own reformulation reads “any two things sharing the same first-order predicate F ...”, but the “two things” is not, strictly speaking, necessary. For the regress can be generated, as I demonstrated above, when starting with just one thing (for instance, Kisen’s poem Sandōkai). I suggest that the “two things” in Schofield’s reformulation is a product of his combining Socrates’s account of participation with (OM).

41 Again, I underline the changes.

42 This task is undertaken in Chapter III.

simply as assertions to the effect that something is qualified in the same or a different way”

(1996, 71). We do not need the Form of Likeness to account for like things being “like” (and mutatis mutandis for the Form of Unlikeness). This, he contends, is illustrated to us in part by an argument from the third deduction that uses the language of pathos, and in part by an argument from the fourth deduction that uses the language of methexis. The former has no difficulty is establishing that like things are “like,” while the latter fails to establish this.

I disagree, as the reason for this difference is not each argument’s language but something else. We begin with the third deduction (157b7-159b2). It opens by noting that the others, as others, are not the One. But these others are not altogether deprived of the

One. Rather, they partake of it in a certain way (metechei pê). Now the others are other than the One because they have parts. Parts belong to that which is a whole, where a whole is one but composed of many, and it is of this that the parts are parts. Important for our purposes is that all of the parts of the whole must partake of the One (anagkê metechein tou henos). For if each of the parts is a part, the word “each” implies that it is one, separated from the rest, and existing by itself. Otherwise it is not an “each.” Thus, from their union (koinônêsantôn) of themselves with the One there arises in each of the others something different within themselves (heteron ti gignesthai en heautois) that gives them a limitation in relation to each other (ho dê peras paresche pros allêla). This stands in contrast to their own natures. For when the others are considered just by themselves and do not partake of the One, their own natures give them no limits (hê d’ heautôn phusis kath’ heauta apeirian). It is in this way that Parmenides lays the foundation for an argument demonstrating that the others are both like and unlike themselves and each other.

The fourth deduction (159b3-160b5) builds towards its argument concerning likeness and unlikeness is a markedly different way. The One is separate (chôris) from the others, and the others are separate from the One. In addition, there is nothing other than these; the phrase “the One and the others” includes all things. Now what is truly one (alêthôs hen) has no parts. But if this is so then the One cannot be in the others as a whole, as it is separate from the others, nor are parts of the One in the others, for it has no parts. Consequently, the others cannot partake of the One in any way. Since this is so, the others are not one in any sense. But neither are the others many; for if they were many, each of them would be one part of the whole. The others, then, are neither many nor a whole nor parts, since they do not participate in the one in any way. This is how Parmenides sets up an argument that concludes that the others are neither like nor unlike themselves or each other, in contradiction with that argument from the third deduction.

What we need notice here is that there are differing accounts of participation present in these two deductions. The third deduction has an account by which the others do partake in the One.43 Hence there is, since each of the others in the third deduction is one, a way of demonstrating that the others are like and unlike themselves and each other.44 But the fourth deduction’s account precludes the others from partaking in any way in the One. Since the others in this deduction are not even one, there is no way for them to be like and unlike themselves and each other. It is a consequence of this deduction’s different account of

43 Notice, though, that its details are not given. All that is said, again, is that the others partake of the One “in a certain way” (metechei pê).

44 I do not deny, as Schofield is certainly correct to point out, that once this demonstration begins the language of methexis altogether disappears. This is all the more curious when it is recognized that up to this point (157b7-158d9) the language of methexis is front and center.

participation that justifies this latter argument’s central premise: that it is impossible for things which do not participate even in one thing to participate in two (that is, Likeness and

Unlikeness). It is not, I submit, the one argument’s use of the language of pathos and the other argument’s use of the language of methexis that explains their contradictory conclusions. This conclusion is reinforced by the fact that even if the argument from the fourth deduction used the language of pathos, it would still fail to demonstrate that the others are like and unlike themselves and each other. Rather, it is the differing accounts of participation in operation in these deductions that accounts for their respective, and contradictory, conclusions.

Now for a more general comment. If the phrase “that which is qualified in the same way is ‘like’” does provide an analysis of likeness and its use in the opening three deductions is without any reference to the Forms, which grounds Schofield’s proposed distinction between first-order predicates and second-order predicates, then, as mentioned above, there is no need for a Form of Likeness. But, Schofield writes, “… would someone who took this line still be a Platonist? Is a Platonism without the Form of Likeness — central to Socrates’s original presentation of the theory at 129a-e — really Platonism? There would be little point in trying to save it from a reduction ad absurdum by abandoning it” (1996, 76).

There is more, though. I wrote above that “likeness” is not the only quality to receive analysis in this dialogue’s second part. Others include but are not limited to: unlikeness, whole, part, round, straight, motion, rest, equality, largeness, and smallness. Not all of these qualities are explicitly said to have a corresponding Form. But equality, largeness, and smallness do have corresponding Forms in the Phaedo (74a ff.; 100e ff.). It gets worse when we recall that in the Sophist Motion and Rest are two of the megista genê, alongside Being,

Sameness, and Difference (254d4-257a13). If an analysis and the alleged absence of the

Form of Likeness from the opening deductions suffices to eliminate it from the catalog of

Forms,45 then for the same reasons should go these others as well. The question is not, then,

“is Platonism without a Form of Likeness really Platonism?” but “is Platonism without all of these Forms, and perhaps many others, really Platonism?”

I am inclined to answer “No.” Moreover, this line of response, while it certainly stops the regress generated in (5), asks too much.46 If there is a less costly and equally well- motivated response, then that is some reason for preferring it to this line. With these concerns raised for restricting Socrates’s account of participation in (1) and (OM) to first- order predicates, I set aside this line of response.

F. “No Explanation by Self-Participation”

If my arguments up to this point are sound, then the lesson to be learned from

Parmenides’s Likeness Regress is that there must be an explanation for Likeness’s being

“like” that is different from the explanation for how it is that things other than Likeness are

“like.” Put differently, the lesson to be learned is that we must reject (NES).

There is evidence in the Sophist that this is in fact the correct line of response. In that dialogue, we learn that at least some Forms participate in themselves. We also learn that

45 It is not clear to me that the Form of Likeness (and Unlikeness, for that matter) is entirely absent from the opening deductions. Consider, for instance, this passage: 140e1- 141a5, especially chronou kai homoiotêtos methexei, hôn elegomen ou meteinai tô heni outh’ homoiotêtos oute isotêtos at 140e5-6.

46 As I wrote above, Schofield himself is aware of this general challenge and notes that assessing the viability of this line of response ultimately requires engaging in a much larger project: determining just what happens to Plato’s Forms after the Parmenides and into the late dialogues.

self-participation is the explanation for self-instantiation.47 On the assumption that the Form of Likeness is characterized by the very quality it constitutes, the explanation for this will be that Likeness participates in itself. And this, as I wrote above, prevents Parmenides from generating his regress. As with Parmenides’s initial regress argument, then, issue is one of explanation.

There is something more, though. Although the rejection of (NES) prevents Parmenides from generating his regress, this does not save the account of participation proposed by

Socrates in (1). Recall that (NES) is entailed by that account of participation because, if self- participation were not excluded as an explanation for how it is that Likeness is “like,” the explanation would be circular, and Likenesses’s being “like” would fail to be explained at all. The result is that in rejecting (NES), the account of participation proposed by Socrates in

(1) is also set aside. It would seem, then, that although the resemblance model of participation is the dominant model throughout Plato’s dialogues, Plato ultimately gives it up in favor of self-participation as the explanation for self-instantiation.48

G. Conclusion

This chapter and Chapter I focused on a pair of regress arguments from the first part of the Parmenides. The dominant response in the secondary literature to them has been that self-instantiation is (or should be) jettisoned from the theory of Forms. My primary concern has been to show that there are good reasons to think that this is not correct, that the lesson to be learned from these arguments is something else. My suggestion has been that these

47 Establishing these conclusions is largely the task of Chapter IV.

48 My paper “Participation in the Parmenides and the Sophist” defends these claims at length.

arguments challenge us to think about how it is that some Forms are characterized by the very qualities they constitute, and why self-instantiation is a continuing component of the theory of Forms. Collectively, then, these chapters serve to motivate the constructive project

I undertake in Chapters III, IV, and V.

The next chapter is concerned with the structure and content of the Parmenides’s second part, where Parmenides gives a demonstration of the method of training that will allow

Socrates to save the theory of Forms. I will present and defend a general interpretation of the exercise, one that reinforces some of the conclusions arrived at in Chapters I and II. In addition, my general interpretation paves the way for our engagement with the Sophist, the principal concern of Chapters IV and V.

III. The Structure and Content of Parmenides’s Exercise

A. Introduction

The previous chapters examined a pair of regress arguments marshaled by Parmenides against the theory of Forms. It is sometimes claimed that the lesson learned from these arguments is that self-instantiation is (or should be) jettisoned from the theory of Forms, that the Forms are not characterized by the very qualities they constitute. I argued that this cannot be the case. Rather, both arguments encourage us to consider both how and why some

Forms self-instantiate.

There is one more challenge to self-instantiation that I wish to consider. Constance

Meinwald has made a sustained case that the central lesson from the second part of the

Parmenides is a distinction between two sorts of predications: predication “in relation to itself” (pros heauto) and predication “in relation to the others” (pros ta alla).49 The former, she claims, do not say of some subject that it displays or exhibits some character or quality

— rather, they reveal the structure of some subject’s nature — while the latter do say that some subject displays or exhibits some character or quality. If this is the case, and if it is only predications pros heauto and not predications pros ta alla that are proper to Forms, then no Form is characterized by the very quality it constitutes. Finally, it is a not unreasonable, further suggestion that Plato is informing his readers of this by distinguishing these two sorts of predications in the second part of the Parmenides. For it is in this part of the dialogue that Parmenides demonstrates how Socrates, training himself in this way, may save the Forms.

While Meinwald’s interpretation of these pros-qualifications (as I will sometimes refer to them) was discussed some in Chapter I, this chapter completes my engagement with it.

Such an engagement is important not simply because of the issue of self-instantiation. It is also important because Meinwald contends that these pros-qualifications figure importantly into the structure of Parmenides’s exercise — the admittedly bewildering dialectical display that constitutes the entirety of the dialogue’s second part — and consequently influence our understanding of the exercise’s content. For this reason, it is imperative that Meinwald’s interpretation of these pros-qualifications is squarely situated within the larger interpretive project concerning the structure and content of Parmenides’s exercise.

Here I shall argue against Meinwald’s understanding of these pros-qualifications, and ultimately against her overall interpretation of the exercise itself. This removes yet another challenge to self-instantiation as a continuing component of the theory of Forms. I will also present an alternative, general interpretation of the dialogue’s second part. An attractive result of this endeavor is its reinforcement of conclusions established in previous chapters.

Finally, it sets the stage for those that follow, where our focus shifts to portions of the

Sophist.

B. Meinwald’s interpretation

How should we understand Parmenides’s seemingly impenetrable dialectical display?

For our purposes, there are two general interpretations. According to one interpretation, the systematic, contradictory conclusions constitutive of the dialogue’s second part are in fact not at all contradictory. Some proponents of this interpretation argue that the individual

49 See Meinwald (1991), (1992), and (2014).

sections of argumentation — what I will sometimes refer to as “deductions” — treat different subjects. While other proponents contend that the deductions treat the same subject but from different perspectives. Thus, Socrates can accept all (or most) of the conclusions from Parmenides’s display, and he learns either a series of important features about different subjects or different sets of facts about the same subject.50 By the other interpretation,

Parmenides presents Socrates with genuine antinomies.51 And although many (but not all) of

Parmenides’s conclusions are validly deduced, the arguments for some of them are nevertheless unsound. Here proponents divide over which conclusions and their supporting arguments stem from faulty assumptions. But all proponents of this interpretation agree that the antinomies are designed to facilitate Socrates’s discernment and rejection of such faulty assumptions concerning Forms.

Meinwald’s interpretation contends that the dialogue’s second part contains only apparently contradictory conclusions. Thus, it is an instance of the first general interpretation. In addition, Meinwald argues that the deductions treat the same subject but from different perspectives. Here is a summary of her case for this: from 134e7-136c5,

Parmenides provides what we may call some “transitional remarks.”52 These remarks bridge the gap between his challenges to Socrates’s position concerning Forms in the dialogue’s first part and a display of the method of training that is promised to help Socrates overcome

50 The Neoplatonists are representatives of this first species of interpretation. More recent proponents include Cornford (1939), Miller (1986), and Sayre (1978), (1983), and (1996). Meinwald is the main advocate of the second species of interpretation, which is defended and expanded in Peterson (1996), (2000), and (2003).

51 This interpretation is proposed by, among others, Russell (1937), Ryle (1939), Friedländer (1969), Owen (1970), Schofield (1977), Allen (1997), and Gill (1996), (2012) 45-72, and (2014).

52 Unless otherwise noted, all references are to the Parmenides.

them in the dialogue’s second part. Important for our purposes is that these transitional remarks outline this method of training. In Chapter I, I wrote that central to Parmenides’s description of the exercise is a pair of qualifications: Socrates must consider the consequences that follow from some positive hypothesis both for the subject in relation to itself and in relation to the others, and then for the others in relation to themselves and in relation to the subject. Then from the negation of this positive hypothesis, Socrates must again consider consequences that follow both for the subject in relation to itself and in relation to the others, and also for the others in relation to themselves and in relation to the subject. Indeed, these pros-qualifications are mentioned as pairs a total of six times in

Parmenides’s varying descriptions of the exercise (136a4-c6). Meinwald suggests that the repeated mention of these pros-qualifications by Parmenides indicates that there is something significant about them.53

When we look to Parmenides’s actual display of this exercise, we find that it consists of eight sections of argumentation.54 The initial four sections derive results for the One and the others from some positive hypothesis, while the remaining four sections derive results for the One and the others from the negation of this positive hypothesis. If we consider

Parmenides’s description of the exercise without attending to these pros-qualifications, then it outlines for us only four sections of argumentation: from the positive hypothesis, what follows for the subject / from the positive hypothesis, what follows for the others / from the negation of this positive hypothesis, what follows for the subject / from the negation of this

53 In addition, the pros-qualifications reappear at the end of the fourth deduction (160b2- 4) and in the summary of the whole exercise at the end of the eighth deduction (166c2-5).

54 Meinwald follows many others in understanding the apparently extra deduction at 155e4-157b4 as an appendix to the first and second deductions. For a short but instructive discussion of this issue see Gill (2012) 48-9, and 49 n. 9 for the relevant bibliography.

positive hypothesis, what follows for the others. But this is half of what the dialogue’s second part actually contains. However, Meinwald points out, if we include these pros- qualifications—that is, if they are understood as contributing to the exercise’s general structure—then Parmenides’s description of the exercise represents all eight deductions found in the dialogue’s second part. This, she maintains, together with the above observation concerning their repetition by Parmenides, counts in favor of the pros-qualifications playing this structural role. Assuming that these pros-qualifications do play this structural role, the structure of Parmenides’s exercise on Meinwald’s interpretation is this (note: “+” stands for the positive hypothesis, if the One is; “−” stands for the negation of this positive hypothesis, if the One is not),

Deduction Hypothesis Subject Qualification

1 + One pros heauto

2 + One pros ta alla

3 + Others pros heauto

4 + Others pros ta alla

5 − One pros heauto

6 − One pros ta alla

7 − Others pros heauto

8 − Others pros ta alla

Notice an upshot of this structure: when qualified in this way, the conclusions deduced by Parmenides in the dialogue’s second part no longer contradict each other. The first and second deductions derive different sorts of conclusions for the subject from the positive hypothesis; the third and fourth deductions derive different sorts of conclusions for the others from the positive hypothesis; and a similar pattern is so from the negation of this

positive hypothesis. Consequently, Socrates and we — the readers — can accept all of the conclusions demonstrated by Parmenides. Moreover, by engaging in this exercise Socrates positions himself to apprehend different sorts of facts about the subject and the others — what is so for them pros heauto and pros ta alla — from the positive hypothesis and the negation of this positive hypothesis.

What are these pros heauto and pros ta alla facts that Socrates will learn by training himself in this way? Put differently how do these pros-qualifications, assuming that they are structural components in Socrates’s method of training, influence the exercise’s content? Let me briefly answer these questions by recalling the discussion of these pros-qualifications from Chapter I. Meinwald contends that in statements of this form “A is B pros C” pros can function either as a syntactic aid indicating that some relation B holds between A and C, or it serves to indicate that some yet unnamed or yet unknown relation bears on A’s being B.55

When it comes to the second part of the Parmenides, Meinwald maintains that these pros- qualifications function in the second way. For predications pros heauto, it is the subject’s position within some genus-species that bears on that subject’s being B. Thus, predications of this sort reveal the structure of some subject’s nature (sometimes Meinwald calls them

“tree predications”) but do not assert of the subject that it displays or exhibits some character or quality. On the other hand, for predications pros ta alla it is the subject’s “conforming to” a nature that is (typically) other that bears on the subject’s being B. These sorts of predications do assert that some subject displays or exhibits some character or quality. And these last as self-predications are true for only some Forms. So, determining what follows for, say, some subject in relation to itself is simply determining what predications are true of

55 For examples of these two functions of pros see Meinwald (1991) 50-1, who draws on Smyth’s grammar and the lexicon of Liddell, Scott, and Jones.

this subject in virtue of its position within some genus-species tree. And determining what follows for this same subject in relation to the others is simply determining what characters it displays as a result of its “conforming to” natures that are (typically) other. Consequently

Socrates, by engaging in Parmenides’s recommended method of training, apprehends facts about the structure of some thing’s nature and facts about the qualities that this same thing exhibits, whether this thing is the subject itself or the others, both from the positive hypothesis and the negation of this positive hypothesis.

C. Critique of Meinwald’s interpretation, part 1

My discussion of Meinwald’s interpretation in Chapter I centered in part on whether

Meinwald had provided sufficient reason for precluding predications pros heauto from asserting that some subject displays or exhibits some character or quality. There I maintained that she had not done so. But my earlier criticisms grant Meinwald that in constructions of the form “A is B pros C” pros indicates some yet unnamed or unknown relation that bears on A’s being B, and does not function as a syntactic aid indicating that some relation B holds between A and C. My primary target in this section is this foundational claim. I shall demonstrate that there is no justification for this function of pros in the dialogue. As a result, the claim on which Meinwald’s entire interpretation depends is without justification. An initial consequence of this result is the removal of another challenge to self-instantiation as a continuing component of the theory of Forms. A further consequence is this: demonstrating that pros functions as a syntactic aid in Parmenides’s exercise, in conjunction with some other matters, provides us with strong reason for outright rejecting Meinwald’s understanding of the exercise’s structure and content.

Let me begin by declaring that throughout Parmenides’s display of the method of training, Parmenides never uses pros in the way required by Meinwald’s interpretation.

Parmenides always uses pros as a syntactic aid, indicating that some relation B holds between A and C. Unsurprisingly, this is not a new observation.56 What is surprising, though, is Meinwald’s continued response that there are two — but just two — passages in the dialogue’s second part where Parmenides does use pros as required by her interpretation.57 The passages appear in the fifth deduction (160b6-163b7). The first passage is an argument that establishes that “the One would have unlikeness, in relation to which the others are unlike it” (161b3-4). The second passage is an argument that establishes that “the

One partakes of inequality, in relation to which the other are unequal to it” (161c9-d1).

Rickless (2007, 104) offers an alternative reading of these lines that results in pros functioning as a syntactic aid. But his arguments turn on matters of punctuation — whether to omit the comma, turning the unrestrictive clauses into restrictive clauses. Since punctuation is not in the original text but added by editors of the manuscripts, perhaps this is why Meinwald remains firmly committed to her reading of these lines. However, the debate need not turn on a comma. Setting aside matters of punctuation, I shall demonstrate that

Meinwald misunderstands these arguments. Consequently, neither passage serves as evidence for her foundational claim. Since these are the only passages that supposedly support Meinwald’s interpretation of the pros-qualifications, demonstrating that they in fact do not leaves the interpretation without any textual support. In addition, my arguments serve

56 For this criticism, alongside some related points, see Gill (1996) 56 n. 90, Sayre (1996) 111-4, Turnbull (1998) 197-9, Rickless (2007) 102-6, Gill (2012) 52 with n. 17, and Gill (2014) 504-505.

57 The passages are first discussed in Meinwald (1991) 56-63. For Meinwald’s continued commitment to her reading of them, see her (2014) at 476-7.

to confirm the above declaration. Since there is no textual support for Meinwald’s contention that pros indicates some yet unnamed or unknown relation that bears on A’s being B, and decisive evidence that pros function as a syntactic aid in Parmenides’s exercise, I submit that we must reject the former in favor of the latter.

Let us begin with the first passage. Here is the argument in its entirety,

Καὶ ἀνοµοιότης ἄρα ἐστὶν αὐτῷ πρὸς τὰ ἄλλα· τὰ γὰρ ἄλλα τοῦ ἑνὸς ἕτερα ὄντα

ἑτεροῖα καὶ εἴη ἄν. — Ναί. — Τὰ δ᾽ ἑτεροῖα οὐκ ἀλλοῖα; — Πῶς δ᾽ οὔ; — Τὰ δ᾽

ἀλλοῖα οὐκ ἀνόµοια; — Ἀνόµοια µὲν οὖν. — Οὐκοῦν εἴπερ τῷ ἑνὶ ἀνόµοιά ἐστι,

δῆλον ὅτι ἀνοµοίῳ τά γε ἀνόµοια ἀνόµοια ἄν εἴη. — Δῆλον. — Εἴη δὴ ἄν καὶ τῷ ἑνὶ

ἀνοµοιότης, πρὸς ἥν τὰ ἄλλα ἀνόµοια αὐτῷ ἐστιν. — Ἔοικεν.

And [the One] has unlikeness in relation to the others. For things other than the

One, since they are different, would also be different in kind. — Yes. — And are not

things different in kind other in kind? — Doubtless. — Are not things other in kind

unlike? — Unlike, certainly. — Well, then, if in fact they are unlike the One, clearly

things unlike would be unlike and unlike. — Clearly. — So the One would have

unlikeness, in relation to which the others are unlike it. — So it seems. (161a6-b4)

Meinwald maintains that here there are two different formulations of the argument’s conclusion. The first conclusion appears at the argument’s outset: “And [the One] has unlikeness in relation to the others” (161a6). The second conclusion appears at the argument’s end: “So the One would have unlikeness, in relation to which the others are unlike it” (161b3-4). She writes that the first conclusion is an instance of pros as a syntactic aid, indicating that the relation of unlikeness holds between the One and the others (1991,

58). However, she maintains that the second conclusion asserts that the others are unlike the

One pros Unlikeness (1991, 58). According to Meinwald this is an instance of pros indicating that some relation yet unknown bears on A’s being B — this yet unknown relation bears on the others’ being unlike. Thus, she concludes that this is an instance of

Parmenides using pros that justifies her interpretation.

This reading of the argument cannot be correct. First, that the argument has two different conclusions is inconsistent with Parmenides’s method throughout the deductions. Frequently

Parmenides announces the conclusion to be derived at an argument’s outset, which is then stated again at the argument’s end. This sort of announcement is all the more common when some particular argument is part of a series of similarly themed arguments. Consider, for instance, the argument at 139c3-d1. This argument is third in a series of four, collectively concerned with sameness and difference. It concludes that the One is not different from another, and indeed Parmenides announces as much at the argument’s outset. He says, “and

[the One] will not be different from another, as long as it is one” (heteron de ge heterou ouk estai, heôs an ê hen, 139c3-4). This same conclusion is repeated, albeit in different language, at the argument’s end. There Parmenides says, “And if [the One] is itself is no way different, it will be different from nothing” (auto de mêdamê on heteron oudenos estai heteron, 139c8-d1). We should expect, therefore, not two different conclusions but the same conclusion.

Second, notice just how different these allegedly different conclusions are. At the argument’s outset, Parmenides announces that he will demonstrate that the One has unlikeness in relation to the others. But at the argument’s end, Parmenides concludes

(according to Meinwald) that the others are unlike the One pros Unlikeness. The difference between the former and the latter is not just that the latter supposedly contains an instance of

pros that indicates that some yet unknown relation bears on A’s being B. In addition, the latter conclusion is about the others while Parmenides’s announces that he shall demonstrate something about the One. This is all the more surprising because the fifth deduction (160b6-

163b7) and the sixth deduction (163b8-164b4) derive consequences for the One from the hypothesis, if the One is not. The Others are not the focus until the seventh deduction

(164b6-165e2) and the eighth deduction (165e4-166c7). Parmenides’s opening remarks for each of these last is explicit about this. Parmenides says at the outset of the seventh deduction, “Let us go on and say what properties the others must have, if the one is not”

(164b4). And then again at the beginning of the eighth deduction, “Let us go back to the beginning once more and say what must be the case, if the One is not, but things other than the One are” (165e4-5). Thus, if Meinwald’s reading of this argument is correct — if by it there are two different conclusions — then Parmenides’s second conclusion is in the wrong place! It should appear in the seventh deduction where positive conclusions are derived for the others from the hypothesis, if the One is not.

What, then, is the correct reading of the argument? After Parmenides announces that he will demonstrate that the One has unlikeness in relation to the others, he imports the consequences of a conclusion established earlier in the fifth deduction (see 160b5-e2). The others, he says, since they are different from the One, are different in kind from the One.

There then follows a series of entailments: if something is different in kind, then it is other in kind; if something is other in kind, then it is unlike. Since the others are different in kind, they are unlike. Next comes the crucial premise: if in fact the others are unlike the One, then clearly these unlike others would be unlike to an unlike. Why does Parmenides formulate the antecedent in this way? Answer: this is what has just been shown — the things that are other than the One are different in kind (from the One), so other in kind (in relation to the One),

and so unlike (the One). But if this last is so, then, since unlikeness is something that holds between (as it is put here) two unlike things, Parmenides infers that the One also has unlikeness, “in relation to which the others are unlike it” (161b4). Perhaps this last is awkward. But it is a mistake to read it as asserting that the others are unlike the One pros

Unlikeness. Unlikeness is predicated of the One in the antecedent, and the consequent asserts that it is in relation to the unlike One that the others are themselves unlike. Put differently, since the unlike others must be unlike in relation to some other unlike, and the

One is that in relation to which the unlike others are unlike, it follows that the One has unlikeness in relation to the others. There are not two conclusions here but just one — the very conclusion that Parmenides said he would demonstrate at the argument’s outset.

Finally, in this conclusion pros functions as a syntactic aid — it indicates that the relation of unlikeness holds between the One and the others.

A similar reading holds for the other passage that allegedly offers some support. Here is that argument,

Καὶ µὴν οὐδ᾽ αὖ ἴσον γ᾽ ἐστὶ τοῖς ἄλλοις· εἰ γὰρ εἴη ἴσον, εἴη τε ἄν ἤδη καὶ

ὅµοιον ἄν εἴη αὐτοῖς κατὰ τὴν ἰσότητα. Ταῦτα δ᾽ ἀµφότερα ἀδύνατα, εἴπερ µὴ ἔστιν

ἕν. — Ἀδύνατα. — Ἐπειδὴ δὲ οὐκ ἔστι τοῖς ἄλλοις ἴσον, ἆρα οὐκ ἀνάγκη καὶ τἆλλα

ἐκείνῳ µὴ ἴσα εἶναι; — Ἀνάγκη. — Τὰ δὲ µὴ ἴσα οὐκ ἄνισα; — Ναί. — Τὰ δὲ ἄνισα

οὐ τῷ ἀνίσῳ ἄνισα; — Πῶς δ᾽ οὔ; — Καὶ ἀνισότητος δὴ µετέχει τὸ ἔν, πρὸς ἥν

τἆλλα αὐτῷ ἐστιν ἄνισα; — Μετέχει.

Furthermore, [the One] is not equal to the others either; for if it were equal, it

would then both be, and be like them in respect of equality. But those are both

impossible, if in fact the One is not. — Impossible. — Since it is not equal to the

others, must not the others, too, be not equal to it? — Necessarily. — Are not things

that are not equal unequal? — Yes. — And are not things unequal unequal to

something unequal? — Doubtless. — So the One partakes also of inequality, in

relation to which the others are unequal to it. — It does. (161c3-d1)

The same criticisms apply here: that there are two different conclusions is inconsistent with Parmenides’s method throughout the deductions; the supposed second conclusion demonstrates something about the others, but Parmenides says that he will demonstrate something about the One; and if the second conclusion is indeed about the others, then this argument is in the wrong deduction.

For the sake of completeness, here is the correct reading of this argument: Parmenides announces that he will demonstrate that the One is not equal to the others. The contrary — that the One is equal to the others — requires both that the One is and that the One is like the others in respect of equality. Yet the hypothesis governing this fifth deduction is, if the One is not. Thus, it is not the case that the One is, and so cannot be like the others in respect of equality. Note Aristotle’s affirmation of this at 161c6: adunata. Now equality, like unlikeness, is something that holds between two things. Since the One is not equal to the others, the others must also be not equal to the One. Once more note Aristotle’s affirmation of this at 161c8: anagkê. But not equal things, Parmenides contends, just are unequal things.

And as with unlikeness, an unequal thing is unequal to another unequal thing. Since the others are not equal (read: unequal) to the One, the One also has inequality, “in relation to which the others are unequal to it” (161d1). Here too the awkwardness of this last is explained by the premise that inequality is a relation between two unequal things.

Nevertheless, the point is clear: since the others are unequal to the One, the One is unequal

to the others. There are not two conclusions here but just one — the very one announced by

Parmenides at the argument’s outset, in which pros functions as a syntactic aid. This passage too is not evidence for Meinwald’s interpretation.

We can extend this critique beyond the Parmenides by briefly turning out attention to

Plato’s Sophist.58 Meinwald contends that her interpretation of these pros-qualifications captures a finding of Frede’s in the Sophist.59 The finding in question is a distinction between two ways of being — auto kath’ hauto and pros alla — central to the Eleatic

Stranger’s argument distinguishing Being and Difference. For our immediate purposes the point of importance is this: according to Meinwald whether the phrases pros heauto and pros ta alla, or auto kath’ hauto and pros alla, are used does not matter. It is the same distinction between two sorts of predications; this is nothing more than varying terminology.60 Yet this cannot be so. First, shortly after the argument distinguishing Being from Difference, we find in a summary of the conclusions the Eleatic Stranger asserting that

“we must admit that Change is the same and is not the same, and we must not be disturbed thereby; for when we say [Change] is the same, we speak in this way because of its participation in sameness in relation to itself (pros heautên)” (Soph. 256a10-b2). This last just is the phrase pros heauto functioning in the same way we find in the Parmenides — indicating that some relation B holds between A and C, where “C” is “A itself.” Here too is there evidence that pros does not function as required by Meinwald’s interpretation. Second, there is good reason to resist Meinwald’s identification of the phrases pros heauto and pros

58 The following is indebted to the discussion in Gill (2012) at 52-3 and 173-6.

59 See Frede (1967) and (1992).

60 See especially Meinwald (1991) 74-75, 178 n. 18, 179 n. 19; (1992) 381-2; (2014) 480-1.

ta alla with the phrases auto kath’ hauto and pros alla respectively. As Frede understands the phrase auto kath’ hauto, it specifies a particular way of being expressible in essential predications. He illustrates this with an example involving Socrates, contrasting being auto kath’ hauto with being pros alla, where this latter is a way of being expressible in non- essential predications. Frede writes,

Socrates is or is a being, for instance, in being white. But white is not something

Socrates is by himself; it is something he only is by being appropriately related to

something else, namely the color white. He only is a being in this particular way, or

respect, namely in being white, by standing in a certain relation to something else,

namely white. He is white, not by being this feature, but by having this feature. He is

white, as we may say, by “participation” in something else. The color, on the other

hand, is said to be white, not by participating in, by having this feature, but by being

it. (1992: 400-1, my emphasis)

But this is not the same as Meinwald’s interpretation of pros heauto. Thus, even if

Meinwald had the correct understanding of this pros-qualification in the Parmenides, it would still not be the same as Frede’s understanding of the phrase auto kath’ hauto in the

Sophist. From this alone it is clear that the phrases pros heauto and auto kath’ hauto do not mean the same thing. Moreover, the fact that pros functions as a syntactic aid in

Parmenides’s exercise (and elsewhere) is further confirmation of this point.

Since the above passages from the Parmenides were the only passages that purported to support Meinwald’s contention that pros indicates some yet unnamed or unknown relation that bears on A’s being B, and they do not in fact support it, the contention has no textual support. This, in turn, confirms that Parmenides never uses pros in the way required by

Meinwald’s interpretation. Rather, he always uses pros as a syntactic aid. Moreover, this is exactly how the Eleatic Stranger uses pros in the Sophist when considering relations among some of the Great Kinds. Since there is no textual support for Meinwald’s interpretation of the pros-qualifications, and decisive evidence that pros function as a syntactic aid in

Parmenides’s exercise (and elsewhere) I submit that we must reject the former in favor of the latter. This in turn removes another challenge to self-instantiation as a continuing component of the theory of Forms. In addition, rejecting Meinwald’s interpretation of these pros-qualifications, I contend, provides sufficient reason for rejecting Meinwald’s understanding of the content of Parmenides’s exercise. Recall that the exercise on this interpretation positions Socrates to apprehends facts about the structure of some thing’s nature and facts about the qualities that this same thing exhibits, whether this thing is the subject itself or the others, both from the positive hypothesis and the negation of this positive hypothesis. But if pros does not function in the way requisite for Socrates’s apprehension of these facts, then this cannot be the exercise’s constructive message.

D. Critique of Meinwald’s interpretation, part 2

What, though, about the exercise’s structure? Are these pros-qualifications nonetheless structural components in Socrates’s method of training? It is difficult to see how this is so, at least as Meinwald understands them. In addition to the above, there is at least this: although

Parmenides mentions these pros-qualifications six times in his varying descriptions of the exercise, they do not appear in the exercise itself as often as one might expect. This is in part because Parmenides sometimes specifies the second member in a two-place relation in the dative or genitive case. Gill (2012, 52) provides the following example from the second deduction: “Furthermore, the One would also itself be so [that is, equal] in relation to itself

(pros heauto): having neither largeness nor smallness in itself, it would neither be exceeded by nor exceed itself, but being equally matched would be equal to itself (simple dative: heautôi)” (150e1-4). In addition, the relative absence of these pros-qualifications from

Parmenides’s display of the exercise is in part due to the type of predicates that figure in it.

These include both relational predicates (for example likeness and unlikeness, and sameness and difference) as well as non-relational predicates (for example one and many, and rest and motion). Together these observations cast some doubt on the significance of these pros- qualifications.

We should also remind ourselves that, rather than just one of these pros-qualifications governing a particular deduction, it is the case that both pros-qualifications appear in seven of the eight deductions and the so-called Appendix. Seven deductions and the Appendix demonstrate that various relations do and do not hold between the One and the others, both in relation to themselves and each other. It is only the eighth and final deduction that does not considers relations that hold between the others in relation to themselves and in relation to the One. But this is explained by the fact that the result of the eighth deduction is that “if the One is not, nothing is” (166c1). There is (or are) no thing(s) because of which certain relations could hold, whether in relation to the thing(s) itself (or themselves) or in relation to other thing(s), precisely because the One is not (read: nothing at all). Collectively, these observations suggest that the pros-qualifications do not play the sort of structural role in

Parmenides’s exercise as proposed by Meinwald. In fact, their actual use by Parmenides in the exercise suggests that the pros-construction itself is not the important item in the exercise’s description. These pros-qualifications, I propose, highlight that Socrates’s undertaking to save the Forms must involve consideration of various structural relations between Forms. Indeed, this is precisely what we should expect given the criticisms leveled

by Parmenides in the dialogue’s first part. Despite the varying forms in which Parmenides’s criticisms appear, all of them set their sights on one of two things: either the oneness of the

Forms — whether their unity or their uniqueness — or the participation-relation between

Forms and perceptible things, and thereby challenge Socrates to reconsider the way in which the Forms are and are not qualified (what I will call below the purity of the Forms).

Consequently, if Socrates is to save the Forms then he must find some way for each Form to be both one and yet many (among other qualifications), and in such a way that does not threaten their unity or uniqueness. And this, in turn, involves careful consideration of how the Forms relate to each other, ultimately a question about participation. It is in this way that the pros-qualifications figure into Parmenides’s exercise.

Meinwald might reply that none of this actually affects her proposal regarding the exercise’s structure. For these observations, true though they are, concern what is present within any given deduction. And Meinwald’s proposal concerns what is outside any given deduction — once more, that any given deduction is governed by just one of these pros- qualifications. So, it is imperative that we step back a bit further, and reflect on those reasons that are more fundamental to her position. The reasons are two in number: first that the exercise contains eight sections of argumentation (plus an appendix), but Parmenides’s description of it outlines only four sections of argumentation. Thus, there is a need to align the description with the display, and the pros-qualifications enable this. Second, the antinomist reading of the dialogue’s second part is not tenable. Thus, we must adopt an interpretation by which the seemingly systematic, contradictory conclusions are only apparent. The pros-qualifications, if understood as governing each section of argumentation in the way presented above, accomplish this too. My response to the latter reason is found in the second part of this chapter, where I present an alternative, general interpretation of

Parmenides’s exercise. There I shall show the tenability and indeed attractiveness of this alternative interpretation, which is antinomist in spirit. There is a sense in which the second part of this chapter just is a response to this second reason, though it also sets the stage for our transition to Plato’s Sophist. For the moment, then, I postpone my response to this concern.

As for the first reason, it is my view that Parmenides’s description of the exercise outlines only four sections of argumentation — four antinomies, as I shall sometimes call them. More importantly, though, there is no need to interpret Parmenides’s description in such a way that it completely forecasts the structure and content of the exercise. Indeed, I maintain that this is just not possible. The description of the exercise cannot explain, for instance, why in the exercise itself Parmenides draws both positive and negative conclusions for the subject and the others from some hypothesis; it cannot explain why there are nine sections of argumentation, even if one of them is correctly understood as an appendix; it cannot explain why each member in some pair of deductions emphasizes a different part of the hypothesis that governs them; it cannot explain why there is a shift to talk of

“appearances” in the seventh and eighth deductions; and it cannot explain why there are different accounts of participation (or no account of participation at all, for that matter) in the deductions, among other things. And although Meinwald writes that since neither

Parmenides’s description of the exercise, nor his display of it, are completely intelligible on their own, and so we must interpret each in the light of the other (1991, 20), it is my contention that she gives too much weight to the description itself. This is not to say that the exercise’s description is altogether unhelpful. It is helpful, but to a point, and too much reliance on it prevents us from appreciating the near-paralyzing beauty and complexity of the ensuing dialectical display.

E. A general defense of the Antinomist approach

The alternative interpretation I propose is a species of the antinomist approach.

Specifically, the interpretation developed, advanced, and defended by Gill.61 She contends that there is a single, overarching argument across the second part’s nine sections of argumentation (note the inclusion of the Appendix) intended to provoke Socrates and us to save the positive hypothesis, if the One is.

Let me begin by saying a few things in defense of the antinomist interpretation generally. It is objected to on a variety of grounds. But I consider the most important objections to be, first, the challenge of identifying the target of the antinomies — just what is Socrates (and we along with him) supposed to reject? Second, if the exercise contains genuine antinomies, then why does Aristotle, Parmenides’s interlocutor for the exercise, not object to any of Parmenides’s assumptions, premises, or conclusions?62 I address each in turn.

The target of the antinomies is relatively easy to identify if we consider the relationship between the dialogue’s two parts. When Socrates introduces the Forms in his conversation with Zeno, he stresses that they are not qualified in the same way as perceptible things. We are both “like” and “unlike” through participation in Likeness and Unlikeness, for instance, but Likeness is not unlike nor is Unlikeness like. Socrates presents Zeno with the following challenge that nicely sums up this aspect of the Forms. He says,

61 See Gill (1996), (2012), especially Chapter 2, and (2014).

62 This Aristotle is not “our Aristotle.” He was later a member of the Thirty Tyrants.

“… if someone first distinguishes as separate the Forms, themselves by

themselves, of the things I was talking about a moment ago — for example, Likeness

and Unlikeness, Multitude and Oneness, Rest and Motion, and everything of that sort

— and then shows that in themselves they can mix together and separate

(sugkerannusthai kai diakrinesthai), I for my part,” he said, “would be utterly

amazed, Zeno. I think these issues have been handled with great vigor in your book;

but I would, as I say, be much more impressed if someone were able to display this

same difficulty, which you and Parmenides went through in the case of perceptible

things, also similarly entwined in multifarious ways in the Forms themselves — in

things that are grasped by reasoning.” (129d7-130a3)

Scholars are divided over what I call the purity of Socrates’s Forms in this passage, and in his introduction of them in general. Does Socrates mean to deny only that any given Form is not qualified by its opposite? For instance, that the One is not many, but it may still be both like and unlike other Forms? Or does Socrates outright deny the Forms bearing any quality other than their own? For instance, that Oneness is only or simply one. As I understand Socrates’s position, he intends the stronger claim — any Form only or simply is its respective character and nothing more than this. Should Socrates allow the Forms to bear other qualities, say the One’s being both like and unlike, it is relatively easy to see how from this it could be demonstrated to bear its opposing quality.63 But whether this or the weaker reading of Socrates’s description is ultimately correct does not matter for our purposes. As

63 A particular instructive instance of this is the entirety of the second deduction (142b1- 155e3), which, once it is granted that the One has being and oneness as parts of it, demonstrates that the One is everything indiscriminately (for instance, the same as itself, the same as another, different from itself, different from another). Of course, these results depend on some controversial assumptions. But without Socrates carefully considering how the Forms can blend with each other, he is not able to avoid this consequence.

Socrates’s describes the Forms, they are pure in at least the sense that no Form bears its opposing quality.

In addition, notice that all of Parmenides’s criticisms in the dialogue’s first part target either the oneness of the Forms (whether their unity or uniqueness) or the participation- relation between Forms and perceptible things. This is so even for Parmenides’s argument against Socrates’s suggestion that the Forms are thoughts (noêma). For the proposal that

Forms are thoughts is made by Socrates to save the oneness of his Forms from the earlier criticisms. Socrates’s own words are proof enough here: “But, Parmenides, maybe each of these Forms is a thought […] and properly occurs only in minds. In this way, each of them might be one and no longer face the difficulties mentioned just now” (132b4-7). Parmenides, by confirming that the Forms are objects of thought, is thereby reinforcing his earlier conclusions that challenge the oneness of the Forms.

When we turn to the dialogue’s second part, we see that each of these three features of

Socrates’s view are in Parmenides’s sights. Parmenides’s demonstration opens with a direct challenge in the first deduction to the Forms’ purity. If the One is only or simply one,

Parmenides’s argues, then the One neither is nor is one, and there is no name, account, knowledge, perception, or opinion of it. When Parmenides asks Aristotle at the deduction’s end if it is possible that these things are so for the One, he replies, “I certainly do not think so” (142a8). Consequently, the second deduction at its outset secures that the One is and is one by the One’s partaking of Being. But now the One is many — it has being and oneness as parts of it — and thus the One is both one and many. Yet Socrates cannot reject this result. Once again, if the One is only or simply one it is nothing at all. Thus, Socrates must

abandon his commitment to the purity of the Forms, allowing that some of them are qualified by their opposites.

The second deduction centers Socrates’s attention on an issue that immediately follows upon his abandoning a commitment to the purity of the Forms. How can Socrates preserve his belief that each Form is one? The deduction opens by showing Socrates that, once he allows the One to partake of being, so that it has being and oneness as parts of it, the One is not one but unlimited in multitude. The deduction’s initial regress argument (142c7-143a3) is straightforward. The One has two parts: being and oneness. But each of these two parts both is and is one. Thus, each part has being and oneness as parts of it, and these parts of the parts also have being and oneness as parts of them, and so on ad infinitum. As Parmenides puts the point, “since it always proves to be two, it must never be one” (142e7-143a1). The second regress argument (143a4-144e7), which follows on the heels of the first, is longer and more complicated. I will not run through it here. Instead, I simply state its conclusion.

Being is distributed among all the things that are, which are countless. But any thing that has a part of being, if it is indeed some thing, is some one thing — it partakes of oneness.

Consequently, Being is distributed among the things that are in parts equal to oneness, since oneness is never absent from being and being is never absent from oneness. It is in this way too, then, that “the One itself, chopped up by being, is many and unlimited in multitude”

(144e3-5). These conclusions are problematic in themselves, as they appear to undermine the One’s oneness. Moreover, they serve as the foundation for all those arguments that follow where the One is demonstrated to be all things indiscriminately, bearing manifold incompatible properties. Finding some way to preserve that the One is one, while at the same time many, prevents these unwelcome consequences.

Lastly, the issue of participation. As I shall argue below, there are many fruitful results in the third deduction. Although it concerns the others, and demonstrates how, though by themselves unlimited, they can bear the opposing property of limit, the approach taken in this deduction can be extended to the One. That is, the third deduction provides us with at least a rough outline of how the One can be both One and many. The fourth deduction undermines these results, and in a sense the culprit is the particular model of participation in operation. It precludes the others from partaking in any way in the One. Separated from the

One, the others are nothing more than an indefinite, indescribable multitude. Although

Socrates must abandon his commitment to the purity of the Forms, he cannot do this without at the same time preserving their oneness. Accomplishing this last turns on confronting the problem of participation. It is only in this way that Socrates can preserve the promising results of the third deduction.

In sum, in the dialogue’s first part that which receives most attention is the connection between the Forms’ purity, their oneness, and the participation-relation. It is precisely this connected trio that we see Parmenides target in the exercise. He moves from purity in the first deduction, to oneness in the second deduction, and in the fourth deduction it is participation that undermines the third deduction’s progress. This suffices for now, and further confirmation is found in what follows.

Still, what about Aristotle? Why does he not object to some of Parmenides’s assumptions, premises, or conclusions if the exercise does contain genuine antinomies?

First, it is simply not true that Aristotle accepts all of Parmenides’s conclusions. Above I mentioned that at the end of the first deduction, Parmenides demonstrates that the One, on the hypothesis, if the One is, in fact no way is nor is one, it has no name, no account, and

there is no knowledge or perception or opinion of it. And when asked whether this is so for the One, Aristotle replies, “I certainly do not think so.” Aristotle tells us that although the conclusions in this first deduction are arguably validly deduced, the arguments for them are nonetheless unsound; we should not accept them. This is the only time that Aristotle rejects

Parmenides’s conclusions. But it comes early on in the exercise, and it signals to us that we too should be on guard for more unsound arguments.

It might be asked, “Why does Aristotle not object more? Why is it that he rejects some set of conclusions only when prompted by Parmenides?” At least part of an answer to these questions starts from Parmenides’s reasons for choosing Aristotle. Among them one in particular stands out: that Aristotle, as the youngest, would give the least trouble (hêkista gar an polupragmonoi, 137b7-8). Aristotle is least likely to be a polupragmôn, a word that

Thucydides uses to describe the Athenian character.64 Athenians, as portrayed in the second speech of the Corinthians, are by nature unable “either to keep quiet themselves or leave others in quiet” (I, 70); a polupragmôn is someone psychologically compelled, if you will, to interfere with another’s plans. Remember now that Parmenides has been asked by Socrates, and begged by Aristotle, Pythodorus, Zeno, and the others to go through the exercise for them, since his own description of it was not entirely clear. Although initially expressing hesitancy — it is a strenuous game after all, and he is no longer young — Parmenides obliges their request. And it is just and only this that that he intends to do: demonstrate the exercise. Parmenides does not want an interlocutor such as Socrates, who in his own way is a polupragmôn. Socrates is likely to interrupt him frequently, pose challenging questions, and perhaps present forceful objections. Aristotle, though, should prove less disruptive an

64 Several of the following observations on polupragmosynê are drawn from Ehrenberg (1947).

interlocutor. He does not object more because he is selected to help facilitate Parmenides’s demonstration of the exercise. Aristotle is meant to say what he thinks, allow Parmenides some time to catch his breath, and nothing more.

F. A sketch of Parmenides’s exercise

With this we return to Parmenides’s exercise. Here is its bare-bones structure, given

Parmenides’s description and demonstration of it.65 There are four sections of argumentation

— four antinomies — two of which start from the positive hypothesis, if the One is, and two of which start from the negation of this positive hypothesis, if the One is not. There is also an Appendix to the first antinomy that attempts to rescue its results by holding that the One can be and not be qualified in various ways at different times. All sections of argumentation, then, are in this sense concerned with the same subject, what might be thought to be (an hêgêsaito einai, 135e) the Form of Oneness.66 The subject for which consequences are drawn changes depending on the antinomy in question: the first and third antinomies consider consequences for the One; the second and fourth antinomies consider consequences for the others.

Parmenides’s demonstration also shows us that each antinomy is composed of two

“claws,” as Ryle called them.67 One claw in each antinomy shows us that various non-

65 This section, along with Sections G and H, are indebted to Gill (2012) 45-72 and (2014).

66 This qualification is significant: it reflects the fact that though Socrates will reason about intelligible things best apprehended by reasoning, and so are candidates for Forms, they will be different in some ways from the Forms as presented by Socrates in the dialogue’s first part. For those Forms ran into several admittedly formidable challenges, and Socrates must rethink his conception of them if they are to be saved.

67 Ryle (1939: 542-3) states his view succinctly in his review of Cornford (1939): “The second part of the [Parmenides] is or is intended to be a reductio ad absurdum argument. 85

relational and relational predicates hold for its particular subject (say, the One is F, G, H, and R and not-R in relation to itself and in relation to the others). Call this sort of section

“the positive claw.” The other claw in the antinomy shows that these same predicates do not hold for its particular subject (say, the One is not F, G, or H, and neither R nor not-R in relation to itself and in relation to the others). Call this sort of section “the negative claw.”

Lastly, the ordering of the positive claw and negative claw is different in the first antinomy.

The negative claw appears first, followed by the positive claw, whereas in the other antinomies it is the positive claw that is followed by the negative claw. The following table represents these findings,

Deduction Hypothesis Subject Consequences

1 + One −

2 + One +

3 + Others +

4 + Others −

5 − One +

6 − One −

7 − Others +

8 − Others −

The two propositions to which it is applied, namely, Unity exists and Unity does not exist, are intended to be univocal. There are four main operations in the argument, and each operation has two ‘claws’; and the two ‘claws’ of each operation are intended to demonstrate antithetical conclusions. And the conclusions of each ‘claw’, taken by itself, constitute, for the most part, logically impossible conjunctions. The subject of the hypotheses is a Form or ‘universal’. The purpose of the second part of the dialogue is to show that some presupposition of the theory of Forms contains a radical logical flaw. And the argument is successful.”

G. An outline of the exercise’s content

Following Gill, I propose that across the exercise there is a single overarching argument.

Here is a short summary of it: all nine sections of argumentation work together to throw the participant from the positive hypothesis, which at first appears untenable, to the negative hypothesis, which is demonstrably false, back to the positive hypothesis, where her attention is centered on the positive claw within which fruitful results show themselves before the negative claw undermines them. The participant’s task is rescuing, and then developing, the fruitful results found in this positive claw from their destruction in its paired negative claw.

The positive claw is the third deduction, and the negative claw is the fourth deduction. Thus, the nine sections of argumentation work together to focus the participant’s efforts on the second antinomy.

Here is a more detailed description: the claws constitutive of the first antinomy both in their own way push the participant to the negative hypothesis, that the One is not. The first deduction (137c4-142a8) shows that on the hypothesis, if the One is, the One neither is nor is one. This is clearly unacceptable, as Aristotle indicates at the deduction’s end. The second deduction (142b1-155e3) shows that the One cannot be and be one (at least, in a certain way) without consequently bearing manifold incompatible properties. For instance, that the

One is both different from the other and itself, and the same as the others and itself at 146a9-

147b10. This too is unacceptable.

The Appendix (155e4-157b5) tries to salvage the results of the first antinomy by suggesting that the One can be both F and not-F at different times. Note the opening remarks,

Let us speak of it yet a third time. If the One is as we have described it — being

both one and many and neither one nor many, and partaking of time — must it not,

because it is one, sometimes partake of being, and in turn because it is not,

sometimes not partake of being? — Necessarily. — When it partakes, can it at that

time not partake, or partake when it does not? — It cannot. — So it partakes at one

time, and does not partake at another; for only in this way could it both partake and

not partake of the same thing. (155e4-11)68

Parmenides relies on the Law of Non-Contradiction and the Law of Excluded Middle, which he restricts to things in time, in this section of argumentation. It is their interplay that renders his attempt at reconciliation unsuccessful. Consider the pair motion and rest (156c1- e7). If the One is in motion at one time, and at rest at another time, it must change from being in motion to being at rest. But when can this happen? When the One changes from being in motion to being at rest it should, Parmenides suggests, be in neither state. Yet this violates the Law of Excluded Middle. He then proposes (156d1-e7) that the change occurs outside time, at an instant (exaiphnês). At this instant of change the One is neither in motion nor at rest. However, there is a contradiction in this instant — something not in motion is at rest and something not at rest is in motion, thus the One in this instant is both in motion and at rest.

Collectively, the first antinomy and the Appendix provide strong (though not decisive) reason to reject the positive hypothesis, if the One is, in favor of the negative hypothesis, if the One is not. For no acceptable results have yet shown themselves — either the One is not

68 For those who would reject the antinomist interpretation of the dialogue’s second part, I submit that this passage is particularly problematic. Why would Parmenides undertake to reconcile the contradictory results of the first antinomy if they are not in fact contradictory?

and is not one, or it has manifold incompatible properties, which cannot be reconciled with each other by supposing that they are true of the One at different times.

The negative hypothesis, however, fares even worse. The third antinomy focuses on the

One, presents the participant with opposing views on the “is not” of the hypothesis, if the

One is not. Put differently, here there are opposing views on not-being. The fifth deduction

(160b5-163b6) treats “is not” or not-being as on par with other predicates (for instance, sameness and difference). Thus, the One requires something to link it to its not-being, namely being, and so the One that is not is shown to partake of both being and not-being

(161e3-162b3). The sixth deduction (163b7-164b4) understands “is not” as, adopting this rather lively image from Owen, “a subject with all the being knocked out of it and so unidentifiable” (1971, 247). Here the One is nothing at all, and so not a possible subject of discourse. The fourth antinomy turns its attention to the others, on the hypothesis that the

One is not. The seventh deduction (164b5-165e1) paints a picture of an unstable world filled with constantly changing appearances, where these things-that-appear bear various properties through their relations to each other. This world is shown to be entirely illusory in the eighth deduction (165e2-166c2). These things-that-appear cannot be many and be different from each other apart from the One. On the hypothesis that the One is not, the result is that nothing is. But this is demonstrably false. As Gill writes, “there is a world to be explained” (1996, 106).

As a result, the participant is thrown back to the positive hypothesis, that the One is. But her focus now is sharper. It is directed at a positive claw in which fruitful results show themselves, which are then undermined in its paired negative claw. This happens in the second antinomy, to which we now turn.

H. The second antinomy

The second antinomy derives conclusions for the others from the hypothesis, that the

One is. The third deduction (157b6-159b1) establishes that the others have various properties, while the fourth deduction (159b2-160b2) has the others bearing no properties at all. But there are many fruitful results in the third deduction, and determining how this is undermined in the fourth deduction merits close scrutiny.

The third deduction succeeds, whereas the Appendix fails, not by attempting to combine the results of the first and second deductions. Rather, it combines their perspectives. We have some familiarity with these perspectives by now, and apart from their appearance in

Parmenides’s exercise, as these are the very perspectives introduced by the Eleatic Stranger in his argument distinguishing Being and Difference: auto kath’ hauto and pros allo. There is the way that the others are themselves by themselves, and there is the way that the others are in relation to the One. The use of these perspectives here suggests — but does not show, because the second antinomy focuses on the others — how the One could be both one and many, an important component of Socrates’s efforts to save the Forms. I contend that we can extend their application here to the One itself, and I shall provide just such an extension below.

We begin, though, with an overview of the third deduction. Its opening arguments

(157b5-158b5) establish the following series of conclusions: the others are indeed other than the One; that they are other because they have parts; that these parts are parts of a whole; that the whole is one thing composed of many; that the parts are one; that the whole and the parts must both partake of the One; that these others, though partaking of the One, are different from the One; that these others that are different from the One are many. Some of

the arguments for these conclusions are incredibly challenging, and I shall not discuss any of them in detail here.69 For my purposes it is not important how these conclusions are established, only that they are established. The remainder of the deduction (158b6-159b2) considers the others both apart from the One and various relations that hold between the others when they come to have a share of the One. It is this stretch of argumentation that I will consider at some length.

After demonstrating the above conclusions concerning the others, Parmenides then undertakes (158b6-c8) to show that the others themselves (whether parts or wholes) that get a share of the One are in fact unlimited in multitude (plêthei apeira). The argument is, roughly, this: at the time in which they get a share of the One, the others are not yet one and do not yet partake of the One; at this time the others are multitudes in which oneness is not present. But what makes them unlimited? If we subtract the very least we can from these multitudes, that which is subtracted is itself a multitude and not one, since it does not partake of the One. Therefore, Parmenides concludes, always when we examine the nature of the others itself by itself (aei skopountes autên kath hautên tên heteran phusin), apart from the One, as much of it as we ever see is unlimited in multitude.

We learn two important things from this short argument. First, there is a way that the others are in virtue of themselves, what the others are themselves by themselves (auta kath’ hauta). By themselves, the others are not one because they are different from the One.70 For

69 For a detailed discussion of some of them, along with the relevant bibliography, see Harte (2002) 122-38.

70 We learn in the fourth deduction (159d4-9) that the others, considered themselves by themselves, are also not many. For if they were many, then each would be one part of the whole. But the others are altogether deprived of the One in the fourth deduction, and so are not one, not wholes, not parts, and thus not many.

this reason, consideration of the others from this perspective reveals them just by themselves to be indefinite multitudes. This, in turn, ultimately establishes their being unlimited in multitude. However, earlier in the deduction Parmenides demonstrated that the others are other than the One because they have parts, are parts of wholes, indeed these things other than the One are one complete whole with parts (157e4-5). The second important thing we learn, then, is that if these things cannot be so for the others in virtue of the way that they are themselves by themselves, then they must be so for them in some other way.

The immediately following argument (158c8-d8) presents this other way. The other way is the others’ communion (koinônêsantôn) with the One, and it is through this communion that something different comes to be in them (en autois). This something different affords the others limit in relation to each other — the parts have limit in relation to each other and in relation to the whole, and the whole has limit in relation to the parts — even though by their own nature, by themselves (hê … autôn phusis kath’ hêauta), they are unlimited in multitude. From this perspective, the way in which the others are in virtue of their relation to another (pros allo), where this other is the One, we learn how something can be in some such way, even when this is not possible for them considered just by themselves (kath’ hauta). The argument’s conclusion confirms that this is so. Parmenides says, “In this way, indeed, things other than the One, taken both as wholes and part by part, both are unlimited and partake of a limit” (158d7-8). What we have across these two arguments, then, is an illustration of two ways of being that allows for some subject (in this case, the others) to bear opposite properties (in this case, limit and unlimitedness). Yet this does not threaten what the others are themselves by themselves — unlimited in multitude — nor are the others, though by their nature unlimited in multitude, altogether deprived of limit.

In addition, we also gain some insight into the One’s structural role in the emerging network of Forms. It is not the only Form, in my view, that does this. But it is arguably the most important Form that plays a structural role. (The other obvious contender is Being.)

Without definiteness, there is no hope of other Forms (for instance, Sameness and

Difference) fulfilling their roles. Indeed, this last is confirmed in the fourth deduction (see below).

Once Parmenides has established that the others bear the opposite properties of limit and unlimitedness, it is relatively easy for him to demonstrate that the others are both like and unlike themselves and each other (158e1-159a6). He asserts at the deduction’s end that it will be no further trouble to find that the others are both same and different, in motion and at rest, and all other opposite properties, given the above.

The fourth deduction undermines the progress made in this third deduction. The chief culprits are Parmenides’s assumption that the One is separate from the others and that if the

One is to be one, it must not be many. Since the One is separate from the others and must be one, and the others partaking of it would fragment it into many, the others do not partake of it. Consequently, the others are not one and there is no oneness in them (159c5-d4).

Parmenides then goes on to show that the others are not many, neither like nor unlike, and so on. By the deduction’s end the others end up much in much the same state as the One at the end of the first deduction — they lack all features because they are not even one.

I. The One

Perhaps it is unfortunate that Parmenides, at the end of the third deduction, does not then show Socrates and us how, say, the One can be both one and many, having demonstrated that the others can be both unlimited and limited in the above way. On the other hand, we

should not expect him to do so. For Parmenides says the following to Socrates in his transitional remarks,

Only a very gifted man can come to know that for each thing there is some kind,

a being itself by itself; but only a prodigy more remarkable still will discover that

and be able to teach someone else who has sifted all these difficulties thoroughly and

critically for himself. (135a7-b3, my emphasis)

Parmenides has generously agreed to demonstrate the method of training that will enable

Socrates and us to see the truth clearly. But this is just the first step, and it is imperative that we heed his call to sift thoroughly and critically through the difficulties for ourselves. It is only in this way that we can confirm for ourselves that there is for each thing some kind, a being itself by itself, and cultivate the ability to teach this to those that doubt the Forms’ existence and that we can know them. Here I shall extend the lessons from the latter-half of the third deduction to the One, in an effort to show how it can be both one and many, and in a way that does not threaten its oneness.

Just as the others are unlimited in multitude themselves by themselves (auta kath’ hauta), so too is the One one itself by itself (auto kath’ hauto). This is what is so for them in virtue of their natures. We might also say that their being in this way is self-explanatory — it is explained entirely by themselves, by the way that they are. Although the One is one, it must also be many. For the others, as the third deduction states at its outset, are not altogether deprived of the One, but somehow partake of it (157c1-2). Indeed, without partaking of the One, the others could not be many, and wholes composed of parts. Thus, there must be some way in which the One is many, so that it can be distributed among the others, allowing for these results.

I suggest that this way is in relation to another (pros allo). Just as the others, though unlimited in multitude themselves by themselves (auta kath’ hauta) were nonetheless limited by partaking in the One (pros allo), so too is the One is not many itself by itself

(auto kath’ hauto) but by partaking of the Many (pros allo). It is in this way that each preserves that which it is in virtue of itself or its nature — its own being is not affected by this — and yet able to bear its opposite property, a precondition (at least, in some cases) for fulfilling its role in the emerging network of Forms.

If we are indeed on the right path, then Socrates will need to abandon the assumption that the One is without parts. Some evidence that Socrates can do this without sacrificing the oneness of the One is found in the Sophist, where the Eleatic Stranger says this regarding the

Different,

The nature of difference appears to me chopped up, just like knowledge. —

How? — Knowledge, too, is one thing, but each part of it, by being set over

something, is marked off and has its own proper name derived [from that object].

Hence there are many so-called arts and sorts of knowledge. — Of course. — So

although the nature of difference is one, the parts of it also have that same feature.

(257c7–d5)

Here the Eleatic Stranger concludes that the nature of the Different is one — a unity and unique — and at the same time has parts, which are also one, and these parts are particular negated things (for instance, the not-beautiful and the not-large). I also note that even if the

One and the others both have parts, and so are both many, and yet are at the same time both one, there is a crucial difference in the way in which they are one. The One is one auto kath’ hauto, while the others are one pros allo. The One’s oneness is self-explanatory, while the

explanation for the others’ being one is their partaking in the One. It is this difference in the subject that allows for these different and distinct explanations of each thing’s being that which it is. Finally, to take another cue from the Sophist, Socrates can still secure that the

One and the others are different from each other. This will not be so because the One is without parts while the others have parts, but because each participates in the Different, and thus each is different from the other in relation to each other. The conclusion is not secured by partlessness and parthood, but by a clarification of that which each is auto kath’ hauto alongside participation in the Different, which, as with the One, plays an important structural role in the emerging network of Forms.

J. Looking back

My analysis in this and the above sections of the play between the third and fourth deductions, I submit, provides some supports a suggestion that I made in Chapter I: that we must consider both how and why some Forms are characterized by the very qualities they constitute. An answer to the how question has been emerging here. As we might put it using the perspectives at work in the third deduction, the One is one auto kath’ hauto, while the other things are one pros allo. This strengthens, I suggest, that rejecting (SI) is not the correct response to the initial regress argument in the dialogue’s first part. Rather, Plato is urging us to reject (NI), as it sets peculiar constraints on when some Form can fulfill its explanatory role. These constraints, as we see here in the second part of the Parmenides and will see in the Sophist, are in no way justified. If I am right about this, then the second part of the Parmenides and the Sophist set constraints on any tenable response to Parmenides’s initial regress argument.

These observations also reinforce a position of mine from Chapter II: it is not the case that a lesson from Parmenides’s exercise is that we can do without the Form of Likeness

(pace Schofield); the exercise does not make a point about the language of methexis versus the language of pathos. Rather, as I wrote there it is the differing accounts of participation at work in each deduction in conjunction with the assumptions that are in operation in them, and these led the third deduction to derive positive conclusions for the others, while the fourth deduction undermines those conclusions. Socrates can retain the Form of Likeness, and allow it to play its role in making things “like” each other just in case they are qualified in the same way. But he must determine how the others can partake of the One. For without the others partaking of the One in some way, there is no Form of Likeness. Worse, there are no Forms at all. This in turn supports my contention that Socrates’s efforts must in part be directed at the problem of participation.

Finally, all of this contributes to my view that Parmenides is pushing Socrates to abandon his position on the Forms’ purity, and find a way that allows at least some Forms to bear their opposing property — the One must be many — and yet in such a way that does not threaten their oneness. Socrates’s eventual success on this front is importantly dependent upon his solution to the problem of participation, as indicated by the fourth deduction. This deduction raises once more a puzzle about participation. Participation of the others in the

One, on the one hand, is necessary for the others to be more than an indefinite, indescribable multitude, but at the same time seems to threaten the oneness of the One by pluralizing it into many.

K. Conclusion

At this chapter’s outset, I wrote that it in part sets the stage for those that follow, where our attention turns to the Sophist. Let me bring our discussion to a close by saying a bit more about this.

Consider the following passage from the third deduction,

But clearly it [each part] would partake of the One, while being something other

than one. Otherwise, it would not partake, but would itself be one. But as it is, it is

surely impossible for anything except the One itself to be one. — Impossible.

(158a3–6, my emphasis)

Gill cites this passage and notes that it serves as evidence for the widespread view that, as she puts it, “being and participation are different sorts of relational ties” (2012, 72).71

Only something other than, say, the One can participate in the one. It is a consequence of this view that the One cannot participate in itself, there is no such thing as “self- participation.” Gill disagrees. She contends that by this dialogue “being” and “participation” have come to name the same relational tie. Consider this passage from earlier in the third deduction,

So since [the others] are other than the One, the others are not the One. For [if

they were the One] they would not be other than the One. — That is right. — And

yet the others are not absolutely deprived of the One, since they partake (metechei)

of it somehow (pêi). — In what way? — In that things other than the One are surely

71 See, for instance, Vlastos (1969) and Lewis (1976) 121-2.

other because they have parts; for if they did not have parts, they would be altogether

one (pantelôs an hen eiê). — That is right. (157b8–c4)

She suggests that here the crucial difference is not “being” versus “participation”; the passage does not display for us two different sorts of relational ties, one for the others and another for the One. Indeed there is just one relational tie here, which we can call either

“being” or “participation,” and instead the difference lies as was suggested above in the subjects. Gill proposes, “if the subject is different from the attribute it partakes of, it can still partake of it somehow, but if the subject is the same as the attribute it partakes of, it is altogether that attribute — the attribute exhausts what the subject is by specifying its entire nature” (2012, 74).72 If this is correct, then, contrary to the widespread view, the Forms can and do participate in themselves; there is “self-participation” in this sense. This reading also has the arguable advantage that self-instantiation is a continuing component of the theory of

Forms.

Obviously, the case for these claims cannot depend entirely on these passages, and it does not. There are several passages in Plato’s Sophist that also support the contention that there is “self-participation” for the Forms. I discuss them at length in Chapter IV. Yet consideration of this issue in conjunction with these passages raises some problems.

One problem is that there is dispute among scholars, who agree that in the late dialogue’s there is self-participation for the Forms, whether all Forms participate in themselves. Nehamas, for example, maintains that self-participation is “optional” (1982,

364). Some Forms will participate in themselves, say, the One and the Different. Others,

72 Some might wonder whether this passage really shows all that Gill says it does. I discuss this issue in Chapter IV.

however, will not participate in themselves, say, Change. Nehamas is able to put forward such a position in part because he does not understand “being” and “participation” as naming the same relational tie. I will argue in Chapter IV against Gill and in support of

Nehamas. It is not the case, I shall show, that all Forms participate in themselves. Self- participation is limited to certain Forms.

In addition, there is this: while some Forms must self-instantiate, there is at least one

Form for which this arguably cannot be so. This is the Form of Change (kinêsis). Or can it?

There is some reason for entertaining this question. First, in the Sophist Change and Rest are precluded from communing with each other (Soph. 254d7-8). But this means that Change is not at rest, because it does not partake of Rest. This is surprising, because it is generally

(perhaps even universally!) assumed that all Forms are at rest (see too Soph. 248d10-e5).

Second, if indeed Change is not at rest, then should not Change be changing? Recall that the premise “if something is not at rest, then it is in motion [read: changing]” was central to

Parmenides’s argument that undermines the Appendix’s effort to reconcile the first antinomy’s contradictory conclusions concerning the One. There Parmenides proposed that the One can change from being at rest to changing (or vice versa) at an instant, which is outside of time. At this instant, the One was neither at rest or changing. But there resulted a contradiction in this instant — something not changing is at rest and something not at rest is changing, thus the One in this instant is both changing and at rest. It would seem, then, that if Change is not at rest then Change must be changing. (Or, and perhaps worse, Change is both changing and at rest!) Third, there is a section of the Sophist often called “the Battle of

Gods and Giants” (Soph. 245e6-249d8). The immediate point of importance is that the

Gods, the friends of the Forms, are pressed by the Eleatic Stranger to concede that there is kinêsis for the Forms too. One argument (Soph. 248d5-e7) pushes for this concession by

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appeal to the Forms’ being sensed or known by some subject. Another argument (Soph.

248e7-249b7) starts from the premise that the realm of the Forms includes change, life, soul, and prudence. If the Gods agree that there is reason (nous), then they must accept that there is life, and soul, and consequently must accept that something changing and change as beings. Rejecting this last eliminates reason (Soph. 249b5-6). Despite their resistance, it seems that the friends of the Forms must allow that there is kinêsis in the realm of being.

This last is reinforced by the Eleatic Stranger’s concluding declaration that the philosopher will reconcile the Gods with the Giants, the materialists who contend that all is in flux. The philosopher, that is, will oblige the children’s plea, finding some way to say “that being (to on) and the all (to pan) are all things unchanged and changed (hosa akineta kai kekinêmena), both together (sunamphotera)” (Soph. 249d2-4). Chapter V considers whether there is in fact kinêsis for the Forms, including whether Change is a changing thing.

With this our focus shifts away from the young Socrates and the venerable Parmenides.

Interestingly, though we leave this pair behind, one member of the pair that will concern us is another youth with a promising philosophical mind, and who bears a striking resemblance to Socrates: the young Theaetetus. The other member is from Elea, and a follower of

Parmenides’s teachings: the Eleatic Stranger. Perhaps this is no coincidence.

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IV. Self-Participation in the Sophist

A. Introduction

This chapter is directly concerned with the how and why of self-instantiation. I made the case in the previous chapters that we must consider how some Forms are instances of themselves. This was effected through discussion of Parmenides’s pair of regress arguments, as well as Constance Meinwald’s interpretation of the qualifications pros heauto and pros ta alla. Finally, I offered an alternative interpretation of the second part of the Parmenides.

This positioned us for the present chapter.

Here I offer my own answer to the how question and defend it against a potential challenge. I will also provide an answer to the why question. My answer to the how question is “self-participation” — just as things other than, say, Difference, are different by participating in Difference, so too is Difference different by participating in itself. My answer to the why question is born from consideration of the second part of the Parmenides together with the Forms’ status as the objects of dialectic, the philosopher’s art. The Forms must have certain “structuring features” to be Forms at all, the objects of knowledge, and graspable by reason.

B. The Evidence

There are two passages in the Sophist that indicate that self-participation is the explanation for some Form’s being characterized by the very quality it constitutes. The first appears in a discussion that begins at Soph. 255e8-9. Here the Eleatic Stranger proposes that he and Theaetetus state their conclusions for each Kind, beginning with Change. It is

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entirely other than Rest, and so is not at rest. But it is through its participation in Being.

Change is also other than Sameness, and so is not Sameness. Then at Soph. 256a7-8 the

Eleatic Stranger says, “But yet we found that it [Change] was the same, because all things partake of Sameness” (alla mên hautê g’ ên tauton dia to metechein au pant’ autou). The

Eleatic Strangers says that Change is the same (as itself) because it partakes of Sameness. In addition, he claims that all things partake of Sameness. These two claims together tell us that

Sameness is the same (as itself) because Sameness participates in itself. How so? Sameness is a thing. Since all things partake of Sameness, it follows that Sameness partakes of itself.

Moreover, just as things other than Sameness are the same (as themselves) through their participation in Sameness, so too is Sameness the same (as itself) through participation in itself.

The second passage comes at the end of an argument that starts at Soph. 255c8-10, where the Eleatic Stranger and Theaetetus consider whether “Difference” (thateron) is a fifth class, whether it and “Being” are two names for one Kind. The argument demonstrates that Difference and Being are indeed distinct Kinds. After this the Eleatic Stranger says,

“And we shall say that it [Difference] permeates them all; for each one is different from the rest not on account of its own nature, but on account of participating in the Form of the

Different” (Soph. 255e3-6). Here the Eleatic Stranger asserts that Difference permeates the five Kinds, and says that each one is different because of its participation in Difference. So,

Difference participates in itself. Moreover, just as Being, Change, Rest, and Sameness are different (from each other) by participating in Difference, so too is Difference different

(from each of them) by participating in itself.73 Thus, we learn in the Sophist not only that

73 Some might question this translation, noting that at Soph. 255e4-5 tôn allôn can be dependent on either heteron or hekaston. (These alternatives are sketched in Nehamas 103

Forms commune with or participate in other Forms, but also that some Forms participate in themselves.

C. Participation in the Parmenides

We saw in Section B that some Forms — at least Sameness and Difference — participate in themselves. Recognition of this raises some questions, one of which is, What does it mean for some Form to participate in itself?

Answering this question requires a definite model of participation, something that is often missing in dialogues where the conversation involves the Forms. Consider, for instance, the discussion of the Forms as causes in the Phaedo. Socrates asserts (Phd. 100d4-

8) that all beautiful things are beautiful because of the “presence of” (parousia), or “sharing in” (koinônia), or however we may describe the relationship, the Beautiful. He will not rely on any particular description of this relationship here, save the safest (asphalestaton): “that all beautiful things are beautiful by the Beautiful” (hoti tô kalô panta ta kala kala).

(1982) 352-3 n. 13.) If tôn allôn is dependent on heteron, then pantôn autôn at 255e3 picks out all of the five Kinds: Being, Change, Rest, Sameness, and Difference. This results in the above translation, a consequence of which is the outright assertion that Difference is different by participating in itself. However, if tôn allôn is dependent on hekaston, then pantôn autôn picks out only Being, Change, Rest, and Sameness. This results in the translation, “and we shall say that it [Difference] permeates them all; for each one of the others [each Kind that is other than Difference] is different, not by reason for its own nature, but because it partakes of the Form of the Different.” This alternative translation appears to offer a different explanation for Difference’s being different.

The first translation is preferable on linguistic grounds — hereton is closer to tôn allôn than hekaston. (See again Nehamas (1982) 352-3 n. 13.) But if this is not decisive, despite appearances even on this alternative translation it is still the case that Difference’s being different is explained by Difference’s participating in itself. (Vlastos (1973) 340 n. 13 recognizes this possibility, but stops short of asserting it.) The contrast between the other Kinds and Difference is that the other Kinds are different by participating in some nature that is other than their own natures (namely, the nature of Difference), while Difference is different by participating in its own nature.

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There is one dialogue, though, that does provide a definite model of participation — in fact, it provides three definite models of participation — and this is the Parmenides. And though each of these models is eventually set aside, this does not preclude them from consideration. Parmenides later tells Socrates that he has met with several difficulties concerning the Forms because he has attempted to mark off (horizesthai) the Forms too soon, before properly training himself. Perhaps after some training Socrates will find some way to save one of these models of participation. In fact, if any of them is compatible with

Forms participating in themselves, then that is a point in its favor.

However, I shall argue that none of definite models of participation from the Parmenides is compatible with Forms participating in themselves.74 From this I conclude that it is not possible to answer the question, What does it mean for some Form to participate in itself?

This negative answer is perhaps disappointing, and one might wonder why the question is worth addressing at all if this is the result. Below in Section D I shall show that this negative answer is in fact important for the view that I am developing in this chapter.

There are two models of participation found in the Whole/Part dilemma (Prm. 130e6-

131e7): either (i) the whole Form, being one, is in each of its many participants (Prm.

131a9-10) or (ii) the Forms are divisible into parts, and any Form’s participants partake of a part, so that in each of them there is only a part of this Form (Prm. 131c6-9). But neither (i) nor (ii) is compatible with self-participation.

It is easy to show that (i) is incompatible with self-participation. By this model of participation, Difference, for instance, would be, as a whole, in each of its participants and,

74 The following rehashes, in part, a discussion from Chapter I.

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as a whole, also in itself. This is impossible. For the container and that which is contained must be different things. Difference cannot be at the same time both contained by itself and that which contains itself. Showing that (ii) is also incompatible with self-participation is a bit more complicated. By this model of participation, Difference is divided into parts, and its parts are distributed among its participants, in the same way that a pie is divided among people at a party. Given this, strictly speaking there is no “Difference” for some part of

Difference to be in, in the same way that the other parts of Difference are in the other participants. At best, some part of Difference could be in another part of Difference. The problem, though, is that a part is just that — a part of Difference, and not Difference itself.

Consequently, neither (i) nor (ii) can help us answer our present question.75

What about the third model of participation, the resemblance model proposed by

Socrates at the outset of Parmenides’s second regress argument (Prm. 132c12-133a7)? Here

Socrates says, “these Forms stand as paradigms, as it were (hôsper), in nature, and the other things resemble (eoikenai) and are likenesses (homoiômata) of them; and this participation for other things in the Forms becomes nothing other than resembling (eikasthênai) them”

(Prm. 132d2-6). By this model of participation, “self-participation” means some Form

75 Some might wonder how this argument bears on the “parts” of Difference that emerge later in the Sophist (257c-259b). The immediate thing to say is this: the problem that I am raising for (ii) is not a problem for parthood itself. Rather, it is a problem that arises when parthood is conjoined with a particular account of participation, where it is also the case that some Forms participate in themselves. Since there is no model of participation in play during the discussion of Difference’s “parts” — indeed, there is no model of participation present anywhere in the Sophist — the discussion of the “parts” of Difference is not affected by this argument.

There are larger questions, though. First, How should we understand this language of parthood used to describe the structure of Difference? Second, Does this introduction of parthood represent a new feature of the theory of Forms? These are important questions, and I plan to address them in a separate piece.

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“resembles” or “is modeled on” (eikasthênai) itself. The explanation for how the Beautiful is beautiful, for example, is that the Beautiful resembles or is modeled on itself. This will not do. For if the Beautiful is beautiful (Phd. 100c4-6) because it resembles or is modeled on itself, then the Beautiful must already be beautiful if resemblance or the-being-of-a-model is in fact possible. But if this is the case, then the resulting explanation is circular, and the

Beautiful’s beauty fails to be explained at all. This third model of participation also cannot help us answer our present question.

Since these are the only definite models of participation in the Platonic corpus, and none of them is compatible with Forms participating in themselves, I conclude that it is not possible to answer the question, What does it mean for some Form to participate in itself?

D. The Limits of Self-Participation

We saw in Section B that at least Sameness and Difference participate in themselves.

This raises another question, Do all Forms participate in themselves or is self-participation limited to certain Forms? My aim in this section and those that follow is twofold: first, I shall argue that self-participation is limited to certain Forms. Second, I will defend this answer by responding to a potential objection. Indeed, most of what follows is concerned with the latter aim.

My argument for the conclusion that self-participation is limited to certain Forms is this,

1. If all Forms participate in themselves, then all Forms are instances of themselves.

2. It is not the case that all Forms are instances of themselves. Therefore,

3. It is not the case that all Forms participate in themselves.

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The crucial premise here is (2). While Being and Oneness, for example, are instances of themselves, Equality and Change, I claim, are not instances of themselves.

Surprisingly, the claim that only some Forms are instances of themselves is controversial. Gill, notably, has an interpretation of how the theory of Forms changes in the

Parmenides and the Sophist, and it is a consequence of her interpretation that all Forms are instances of themselves. Specifically, this consequence is a direct result of Gill’s claim that in these later dialogues, “‘being’ and ‘participation’ name the same relational tie” (2012,

72). I shall explain just what Gill means by this below. The immediate thing to say, though, is that Gill misunderstands the passages that she marshals in support of this claim. Put differently, my response to Gill’s potential objection is that none of the passages she cites as evidence for “being” and “participation” naming the same relational tie are in fact evidence for this claim. As a result, there is no textual support for it. Since this is the case, we are without reason to think that all Forms are instances of themselves. Therefore, my argument for the conclusion that self-participation is limited to certain Forms stands firm.

E. My Argument

Let us return to the evidence for self-participation discussed in Section B. We saw that just as Change is the same (as itself) by participating in Sameness, so too is Sameness the same (as itself) by participating in itself. In addition, we saw that just as Being, Change,

Rest, and Sameness are different (from each other and Difference) by participating in

Difference, so too is Difference different (from the other Kinds) by participating in itself.

These observations tell us that self-participation is the explanation for some Form’s being an instance of itself. Sameness and Difference are instances of themselves because each participates in itself, just as other things are instances of them by participating in them.

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While some Forms are undoubtedly instances of themselves — for example, Being,

Oneness, Sameness, Difference, Rest, Likeness, and Unlikeness — other Forms arguably are not. It is a category mistake to maintain that Largeness is large, Smallness small, or Equality equal. In addition, the Forms are immutable. Therefore, it is not the case that Change is changing. If this is correct, then given that the former class of Forms are instances of themselves, while the latter class arguably does not self-instantiate, and self-participation is the explanation for self-instantiation, I conclude that self-participation is limited to certain

Forms because only some Forms are instances of themselves.

F. Gill’s Challenge

My argument for the conclusion that self-participation is limited to certain Forms depends on the premise that only some Forms are instances of themselves. I wrote above that this premise is controversial. It is a consequence of Gill’s reading of the Parmenides and the Sophist that all Forms are instances of themselves. This is the case because, she claims, by the time of the Parmenides and the Sophist “‘being’ and ‘participation’ name the same relational tie” (2012, 72). What does this mean? As I understand Gill, this means that there are two possible explanations — “being” and “participation” — for how some thing instantiates some quality, and which explanation applies in a particular case is determined by the subject in question.

Here is an illustration: my cat Wilbur is different from me. And the explanation for his being different from me is his participation in the Form of Difference. The participation relation links Wilbur with the Form of Difference, with what difference is. As a result, he is an instance of Difference, and so is different from me (and from everything else). Now the

Form of Difference is also different. It is different from Wilbur, from me, and from

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everything else too. However, the explanation for Difference’s being different is not the same as the explanation for Wilbur’s being different, although what is explained is the same

— why each thing is different from the other, and everything else too. The explanation for the Form of Difference’s being different is simply its being what difference is. Difference is

“the what-it-is-to-be different,” and that, all on its own, explains its being different from everything else.

Here is how Gill puts the point,

[…] the crucial difference in the two cases concerns the nature of the subject: if the

subject is different from the attribute it partakes of, it can still partake of it somehow, but

if the subject is the same as the attribute it partakes of, it is altogether that attribute —

the attribute exhausts what the subject is by specifying its entire nature. (2012, 74)

She writes a bit later that in the latter case, “[the] Form and its nature [are] numerically, as well as qualitatively, the same” (2012, 75). As a result “[the] Form can be self- explanatory — be what it is in virtue of itself (auto kath’ hauto) — without depending on anything outside itself to explain what it is” (2012, 75).

It is an immediate consequence of Gill’s claim that in these later dialogues “‘being’ and

‘participation’ name the same relational tie” (2012, 72) that every Form is an instance of itself. Here is why: if some Form’s being the Form that it is is the explanation for that

Form’s being an instance of itself, then all Forms, being the Forms that they are, are for that reason instances of themselves. As a result, Being, Oneness, Sameness, Difference,

Likeness, and Unlikeness are all instances of themselves because each is the Form that it is.

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However, by this line of reasoning it is also the case that Largeness, Smallness, Equality, and Change are instances of themselves, because they too are the Forms that they are.76

Some will find this result sufficient for rejecting Gill’s claim regarding “being” and

“participation.” Others, though, may not be so quick to dismiss it, even if they are themselves hesitant to accept that Largeness, Smallness, and so forth, are instances of themselves. So, we had better see the evidence that led Gill to the above conclusions.

G. A Comparison

Before we see the evidence, though, I want to take this opportunity to contrast Gill’s position with my own. I argued in above that only some Forms participate in themselves because only some Forms are instances of themselves. Gill, on the other hand, is committed to all Forms being instances of themselves because she understands “being” and

“participation” as naming “the same relational tie” (2012, 72). The disagreement between us concerns the truth of this latter claim. Whereas Gill holds that there are two explanations for some thing’s instantiating some quality, I maintain that there is just one explanation — the participation relation. Some Form’s being the Form that it is does not, on my view, result in that Form’s being an instance of itself. It is a necessary condition for self-instantiation, but not sufficient for it. The Form must also participate in itself to be an instance of itself, just as

76 Some might wonder if this is a correct representation of Gill’s position. Does she in fact maintain that Largeness is a large thing, Smallness a small thing, and so forth? Yes, and the reason is not just that, on her view, “being” and “participation” name the same relational tie. Gill also argues that Plato remains committed in the late dialogues to what I call below the “Synonymy Principle.” (I discuss this principle at some length below.) This principle appears for the first time at Phd. 101a8-b2. Gill writes that by this principle, “the cause of F- ness has the character that it explains in its effects” (2012, 23; the entire discussion from 21- 5 is relevant here). Since the Synonymy Principle is a causal principle that applies to all Forms, each and every Form must have the character that it explains in its effect. Therefore, 111

other things participate in it to be an instance of it. Put differently, in my view it is one thing for some Form to be the Form that it is, and another thing for that Form to have its own character. For Gill, by contrast, these two states are in fact one and the same.

It seems that Gill has an explanatory advantage. She can explain how some Form is an instance of itself with the answer, Because it is the Form that it is. Difference is different, for instance, because it is “what difference is.” My explanation is not nearly as straightforward:

Difference is different because it participates in itself. And for the reasons given in Section

C, I cannot answer the question, What does it mean for Difference (or any Form, for that matter) to participate in itself? However, my view has its own advantages. Whereas Gill is committed to all Forms being instances of themselves — including Largeness, Smallness,

Equality, and Change — I can avoid this arguably undesirable conclusion. Since I maintain that it is one thing for some Form to be the Form that it is, and another thing for that Form to have its own character (by participating in itself), on my view it is possible that only some

Forms participate in themselves because only some Forms are instances of themselves. Once more, it is a category mistake to say that Largeness is large, Smallness small, or Equality equal. In addition, the Forms are immutable. For this reason, it cannot be the case that

Change is changing. Below I will offer another reason in support of the claim that only some

Forms are instances of themselves.

H. Gill’s First Argument

Gill cites three passages in support of her position: Soph. 258b11-c4, Prm. 158a3-6, and

Prm. 157b8-c4. We will begin with the passage from the Sophist. However, understanding

it is not only Being and Oneness that self-instantiate. It is also Largeness, Smallness, and so on. 112

its role in Gill’s first argument requires that I say some things about the Forms in the

Phaedo.

At Phd. 100b, Socrates describes the Forms as causes of certain effects in the sensible world. Specifically, the Forms cause things in the sensible world to be qualified in some way. One example that Socrates gives concerns beautiful things, and he asserts that they are beautiful for no other reason than that they share in (metechei) the Form of Beauty (Phd.

100c4-6; 100c9-e3). Socrates then puts forth three principles of causation, one of which is important for our present purposes. This is the principle found at Phd. 101a8-b2, which, as

Gill puts it, states that “the cause of F-ness has the character that it explains in its effects”

(2012, 23). Call this the “Synonymy Principle.” By the Synonymy Principle, the Form of

Beauty, which is the cause of the beauty of all beautiful things, is itself beautiful. Put differently, by this principle the Form of Beauty is an instance of itself. It is a consequence of this that the following statement is true, “the Beautiful is beautiful.” And although

Socrates speaks of only a handful of Forms in this section of the Phaedo, it is clear that his discussion applies to all Forms. Thus, by the Synonymy Principle, every Form, as the cause of sensible things being qualified in some way, is an instance of itself. As a result, statements of the form “the F is F” — what are often called “statements of self-predication” in the secondary literature — are true for all Forms.

This brings us to our passage from the Sophist. It comes as the Eleatic Stranger and

Theaetetus complete an important step in their investigation into not-being. The Eleatic

Stranger asserts that

Just as the large is large and the beautiful is beautiful and the not-large is not large

and the not-beautiful is not beautiful, so too in the same way not-being (to mê on) was

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and is not being (mê on), one form (eidos) numbered among the many beings. (Soph.

258b11–c4)

This passage contains a string of statements of self-predication, which, as we just saw in our brief discussion of the Phaedo, are a consequence of the Forms’ being instances of themselves. And this latter is itself a consequence of the Synonymy Principle. Here is the conclusion that Gill draws from this passage,

Given Plato’s continued reliance on self-predication in his later dialogues, it seems

highly unlikely that he abandoned the [Synonymy Principle] in dialogues responding to

the Parmenides. But if he retained that causal [principle], a Form and its participants

have the same character and have it in the same way (though the Form has it more

eminently), and so “being” and “participation” should name the same relational tie.

(2012, 73)

She reasons from the presence of statements of self-predication at Soph. 258b11-c4 to

Plato’s continued commitment to the Synonymy Principle. But if Plato remains committed to the Synonymy Principle, then the Forms as causes have the characters that they explain in their effects. The Forms — all of them — are instances of themselves. Therefore, “being” and “participation” name the same relational tie.

My response centers on Gill’s claim that in this passage from the Sophist contains a string of “statements of self-predication.” The label “statements of self-predication” is inspired by Vlastos’s classic article on Parmenides’s initial regress argument (Prm. 132a1- b3), otherwise referred to as the Third Man Argument.77 Vlastos argues that, in addition to

77 Vlastos (1954).

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what is explicitly stated in the text, two additional assumptions are required for Parmenides to undermine Socrates’s belief that each Form is one. He called one of these assumptions the

“Self-Predication Assumption,” which states that “any Form can be predicated of itself.

Largeness is itself large. F-ness is itself F” (1954, 324). Vlastos’s introduction of this assumption led many scholars to examine statements of the form “the F is F” in the Platonic corpus. Do all instances of statements of self-predication assert that some Form is an instance of itself? The last sixty years of scholarship shows us that the answer is, No. It is arguable that there are four different types of statements of self-predication, and which is present in a particular case is determined by the context.

Here is my proposal,

We begin on the left. Cherniss, among others, argues that statements of the form “the F is F” are in fact identity statements. He cites Prm. 157b8-c4 as evidence for this claim, writing that there

[…] Plato clearly distinguishes two meanings of “is x,” namely, (1) “has the

character x” and (2) “is identical with x”; assumes that whatever “is x” in one sense is

not x in the other; and states that αὐτὸ τὸ x and only αὐτὸ τὸ x “is x” in the second sense.

As applied to […] the doctrine of ideas generally, this is to say: “the idea of x is x”

means “the idea of x and x are identical and therefore the idea of x does not ‘have the

character x’.” (1957, 258-259)

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We will consider whether this is the case below when our attention turns to Prm. 157b8- c4 and another passage from the second part of the Parmenides.78

Some scholars disagree with Cherniss, specifically with the contention that statements of the form “the F is F” never say of some Form that it is an instance of itself. Nehamas, for example, argues that 255e3-6 is a passage where the statement “Difference is different (from

Being)” does say of Difference that it is an instance of itself, and in this I agree with him.

We also saw in Section B that the statement “Sameness is the same (as itself)” says of

Sameness that it is an instance of itself, and similar statements concerning the One and

Being are found in the second part of the Parmenides. Call these “statements of self- instantiation.” Still, Nehamas argues that it is not the case that all statements of the form

“the F is F” are statements of self-instantiation. Some say something about the Form’s nature — that the F is “the what-it-is-to-be F” or “what F-ness is” — and in this he has been followed more recently (though not for the same reasons) by Meinwald.79

Finally, there are some statements of the form “the F is F” that are not about Forms at all. Vlastos would later argue that for some statements of this form “their predicate-term is asserted not of their abstract subject, but of the concrete instances of that abstract” (1973,

252). He cites this sentence from Iris Murdoch as an example,

78 Cherniss also argues that additional evidence is found in the “Third Bed Argument” of Rep. X, which I shall not discuss here. Both this passage from the Republic and the passage from the Parmenides are central to his attempt to show that both of Parmenides’s regress arguments are unsound. See Cherniss (1957) 258-263.

79 See Nehamas (1979) and (1982), 352-365, and Meinwald (1991), especially 46-75, (1992), and (2014).

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The best kind of courage (that which would make a man act unselfishly in a

concentration camp) is steadfast, calm, temperate, intelligent, loving … (1970, 57)

Vlastos asserts,

Clearly, the reading that ascribes the adjectives, “steadfast, calm,” etc., not to the

abstraction, “best of kind of courage,” but to those persons, if any, who have that kind of

courage; that is clearly what we would understand Iris Murdoch to be saying: that those

who have the best kind of courage, they are “steadfast, calm, temperate, intelligent,

loving,” in their courage. (1973, 253)

He also invites us to consider St. Paul’s statement that “Charity suffereth long and is kind.” Here Vlastos writes,

We may be certain that everyone who has ever read or heard that sentence before

philosophical grammarians got hold of it has taken it, as a matter of course, to be

predicating long-suffering and kindness of those who have the virtue of charity. It would

have taken satanic perversity to construe the apostle to be imputing those moral

properties to an abstract entity. (1973, 253)

He brings this interpretation of some statements of the form “the F is F” to bear, for instance, on the statements “Justice is just” and “Piety is pious” at Prot. 330c-d. Vlastos argues that these statements in this context do not say of the Form of Justice or the Form of

Piety that they are instances of themselves. In addition, he claims that these statements are not about Forms at all. Rather, in this context the statement “Justice is just” says that all concrete instances of justice are just, and the statement “Piety is pious” says that all concrete

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instances of piety are pious. Statements of this sort are commonly called in the literature

“Pauline predications,” after St. Paul.

Distinguishing these different types of statements of self-predication does not by itself show that Gill has misunderstood our passage from the Sophist. For she can say, “Fair enough, I should not have described this passage as containing a string of statements of self- predication. I should have said that it contains a string of statements of self-instantiation.

Still, my claim stands firm — this passage is evidence that Plato remains committed to the

Synonymy Principle. Therefore, all Forms are instances of themselves. Consequently,

‘being’ and ‘participation’ name the same relational tie.” But distinguishing these different types of statements of self-predication is only the first step in my response. The second step is showing that our passage from the Sophist in fact contains statements about the natures of the Large, the Beautiful, and (the parts of) Difference. I maintain that these statements, when read in context, do not assert that these Forms are instances of themselves. The result is that this passage is not evidence for Plato’s continued commitment to the Synonymy Principle.80

Therefore, Gill cannot conclude from this passage that “’being’ and ‘participation’ name the same relational tie” (2012, 72).

We begin at 257b10. Here the Eleatic Stranger and Theaetetus declare that they will not admit that the negative particle (apophasis) signifies (sêmainein) the opposite (enantion).

Rather, they will admit only that the particles “not” and “non-” (to mê, to ou) indicate something different from the words that they are set before (protithemena) or, put differently, from the things to which the names following the negation apply.

80 In fact, if I am right that self-participation, and so self-instantiation, is limited to certain Forms, then Plato does not remain committed to the Synonymy Principle in the late dialogues.

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With this established, the Eleatic Stranger proposes that he and Theaetetus consider something else: whether the nature of Difference is cut up into small parts

(katakekermatisthai), just like knowledge. The Eleatic Stranger explains that knowledge is one (mia), but that each part of knowledge applies to a particular subject and has a name of its own. It is for this reason that there are many arts (technai) and sciences (epistêmai). He then proposes that, in just the same way, Difference is one, but that each part of the nature of

Difference applies to something specific and has a name of its own. For example, there is a part of Difference that is opposed to (antitithemenon) Beauty. This part is called “not- beautiful” (mê kalon), and it is nothing other than what is different from the nature of Beauty

(touto ouk allou tinos heteron estin ê tês tou kalou phuseôs).

The Eleatic Stranger concludes from this (257e2-12) that the not-beautiful is a distinct part of one kind of being (namely, Difference) and that at the same time it is opposed to one kind of being (namely, Beauty). Both the not-beautiful and Beauty are, and equally so. This same line of reasoning is true of the not-large and Largeness, and of the not-just and Justice

(258a1-7), from which he generalizes, saying,

And we shall, then, say the same of other things, since the nature of Difference is

proved to possess real being; and if it has being, we must necessarily ascribe being in no

less degree to its parts also. […] Then, as it seems, the opposition of the nature of a part

of Difference, and of the nature of Being, when they are opposed to one another, is no

less truly existence than is Being itself, if it is not wrong for me to say so, for it signifies

not the opposite of Being, but only the other of Being, and nothing more. (258a8-b5)

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Theaetetus responds, Saphestata ge, “Perfectly clear.” This last quotation is particularly important, as it is here that the Eleatic Stranger and Theaetetus find not-being, which they were in search of because of the Sophist (258b8-9).

All of this brings us to the passage of interest, which I quote in full,

And is this [not-being], as you were saying, as fully endowed with being as anything

else, and shall we henceforth say with confidence that not-being has an assured existence

and nature of its own? Just as we found that the Large was large, and the Beautiful was

beautiful, and the not-large not large, and the not-beautiful not beautiful, shall we in the

same way say that not-being was and is not being, to be counted as one form among the

many beings? Or have we, Theaetetus, any remaining distrust about the matter? — None

whatsoever. (258b10-c7)

The discussion leading up to this passage helps us see that none of these statements of self-predication should be understood as statements of self-instantiation. All of them are statements about the natures of certain Forms. The statement “the Large was large” means

“the Large is and has a nature of its own”; “the Beautiful was beautiful” means “the

Beautiful is and has a nature of its own”; “the not-large is not large” means “the not-large is and has a nature of its own”; “the not-beautiful is not beautiful” means “the not-beautiful is and has a nature of its own”; and in just the same way, “not-being is not being” means “not- being is and has a nature of its own.” These are statements that, when understood in context, assert that the subject — whether some Form or some part of Difference — is and has a nature of its own.

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Since there are no statements of self-instantiation in this passage, this passage is not evidence for Plato’s continued commitment to the Synonymy Principle. For this reason, I submit that this passage does not support Gill’s claim that in the Sophist “‘being’ and

‘participation’ name the same relational tie” (2012, 72).

I. Gill’s Second Argument

Let us turn now to Gill’s second argument for the claim that “’being’ and ‘participation’ name the same relational tie” (2012, 72). This argument depends on two passages from the second part of the Parmenides: 157b8-c4 and 158a3-6. Both passages are part of the third deduction. The first passage, Gill writes, “helps show that ‘being’ and ‘participation’ label the same relation tie” (2012, 73). We will see the argument for this assertion in a moment.

The correct interpretation of the second passage has been much debated in the literature. I wrote above that Cherniss, for example, finds in it a distinction between two meanings of “is x,” one of which is “is identical with x,” and that the passage is central to Cherniss’s argument that statements of self-predication are just identity statements. Gill disagrees — she argues against Cherniss’s interpretation by showing how the second passage in fact agrees with her interpretation of the first passage. This, she concludes, provides some confirmation for her interpretation of the first passage, and as a result the claim that “being” and “participation” name the same relational tie.

While I agree with Gill that Cherniss misunderstands Prm. 158a3-6 — Cherniss does not discuss Prm. 157b8-c4 — I shall argue that Gill too misunderstands these passages. In addition, I will offer yet another interpretation of these texts that is born from consideration of their roles in the third deduction. The result is that, just as with Soph. 258b11-c4, neither passage supports Gill’s claim that “‘being’ and ‘participation’ name the same relational tie”

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(2012, 72). It is a consequence of this that Gill’s claim is without textual support, from which I conclude that, pending additional evidence, we should reject it.

Here is our first passage,

So, since they [the others] are other than the One, the others are not the One. For

then they would not be other than the One. — That is right. — And yet the others are not

absolutely deprived of the One, since they partake (metechei) of it in a certain way (pêi).

— In what way? — In that things other than the One are surely other because they have

parts; for if they did not have parts, they would be altogether one (pantelôs an hen eiê).

— That is right. (Prm. 157b8–c4)

As Gill understands this passage, Parmenides begins by establishing that the others are not identical with the One. He then states what appear to be two predications: the first, that the others partake of the One in a certain way; the second — a counterfactual — that if the others did not have parts, then they would be altogether one. She concludes from these observations that “the crucial difference in the two cases concerns the nature of the subject: if the subject is different from the attribute it partakes of, it can still partake of it somehow, but if the subject is the same as the attribute it partakes of, it is altogether that attribute — the attribute exhausts what the subject is by specifying its entire nature” (2012, 74).

This brings us to our second passage,

But clearly it [each part] would partake of the One, while being something other than

one. Otherwise, it wouldn’t partake, but would itself be one. But as it is, it is surely

impossible for anything except the One itself to be one. — Impossible. (Prm. 158a3–6)

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Recall that Cherniss claims that in this passage Plato distinguishes between two meanings of “is x” — “is predicatively x” and “is identical with x” — and says that they are mutually exclusive. Anything that is predicatively x cannot be identical with x, and anything that is identical with x cannot be predicatively x. Cherniss is certainly mistaken about this latter. As Vlastos pointed out (1981, 336-7), Cherniss’s interpretation requires that the One is not one — it is not marked off from everything else. This is unacceptable. Just as other things are individuated — are one Form, one thing, an “each,” a “this” — through their participation in the One, so too is the One one; the One is one Form, one being, and so forth.

What of the distinction between “is predicatively x” and “is identical with x” that

Cherniss claims to find here? Gill disagrees. She brings the conclusion drawn from the earlier passage to bear on this passage, writing, “this passage makes good sense when read in light of the earlier passage. The others merely partake of the one, since they are one but other than the one, whereas the one is altogether one, because the form and its attribute are the same. There is no difference in the relational tie. The difference concerns the subject — whether it is different from or the same as the character it partakes of” (2012, 74). These two passages from the Parmenides together show, Gill claims, that “‘being’ and ‘participation’ name the same relational tie” (2012, 72).

Once more, I agree that Cherniss misunderstands Prm. 158a3–6. But I maintain that Gill also misunderstands this passage, as well as Prm. 157b8–c4. So, I had better explain why this is the case.

Both passages appear within the third deduction (Prm. 157b7-159b2), which is concerned to derive consequences for the others from the hypothesis, if the One is (Prm.

157b9-10). The deduction falls into two parts. The first part (Prm. 157b7-158b4) addresses

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the question, In what way(s) are the others one? (Prm. 157c2: pêi dê;). The answer is that the others are one is two ways: as a single whole (Prm. 157d8-e6), and as parts of that whole

(Prm. 157e6-158a3; see also 158a7-10). The second part (Prm. 158b5-159b2) answers the question, How are the others one, since by themselves they are without limit? Here the answer is that while the others are in virtue of their own natures without limit, by partaking in the One they become limited in relation to each other (Prm. 158d3-7).

As part of the third deduction generally, we should not expect either Prm. 157b8-c4 or

158a3-6 to say anything about the One itself. Anything said about the One is said only in comparison with, or in contrast to, the others, since the stated aim of this deduction is to derive conclusions for the others, not for the One. In addition, both passages fall within the deduction’s first part. Recognition of this point is important. The concern of the deduction’s first part is demonstrating the ways in which the others are one. It is not part of this portion of the deduction to demonstrate that the One is one, even though the One is one, nor is it to demonstrate how the others or the One are one. How the others are one is explained in the second part of the deduction, and how the One is one is not found at all, as it falls outside the scope of this deduction’s guiding questions. This by itself casts doubt on Gill’s claim that these passages provide evidence that that “‘being’ and ‘participation’ name the same relational tie” (2012, 72).

There is more, though. Let us see Prm. 157b8–c4 again,

So since they [the others] are other than the One, the others are not the One. For then

they would not be other than the One. — That is right. — And yet the others are not

absolutely deprived of the One, since they partake (metechei) of it in a certain way (pêi).

— In what way? — In that things other than the One are surely other because they have

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parts; for if they did not have parts, they would be altogether one (pantelôs an hen eiê).

— That is right.

Parmenides’s first move is establishing that the others are not identical with the One on semantic grounds. The others, as their name suggests, are other than (or, not identical with) the One. If this were not the case, then “the others” would not be the others. Rather, “the others” would be the One. This semantic point only goes so far, however. Specifically, it does not provide Parmenides with the resources he needs to answer the question, In what way(s) are the others one? And remember that it is shown in this deduction’s first part that the others are one as a single whole and as parts of that whole. It is for this reason that

Parmenides follows the semantic point with an argument establishing that the others are not identical with the One on metaphysical grounds. The others are other than the One because they have parts. If the others did not have parts, he asserts, then they would be altogether one.

This line of reasoning recalls the opening moves of Parmenides’s entire demonstration.

At Prm. 137c4-d5, it is asserted that the One, as one, cannot be many. But if the One is not many, then it has no parts and is not a whole. Why? A part is part of a whole, and a whole is that of which no part is missing. But if the One had parts, those parts would be part of a whole. So, the One would be a whole. Or, to reason in the other direction, if the One were a whole, then the One would have parts. Parmenides points out, though, that in either case the

One would be many and not one. Therefore, the One, as one, is not a whole and has no parts.

With this in mind, read once more Prm. 157c2-4: “things other than the One are surely other because they have parts; for if they did not have parts, they would be altogether one

(pantelôs an hen eiê).” If the others did not have parts, and so were not a whole, then the

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others would not be many. But if the others are not many, then they would be altogether one.

The phrase pantelôs an hen eiê should be understood here as “be the One.” The others, lacking parts, would be identical with the One; they would be the One.81 None of this, though, says anything about how the others are one or how the One is one. Much less does

Parmenides say that it is through participation in the One that the others are one, and that it is in virtue of the One’s being the One that the One is one. I submit that this passage is not evidence that, as Gill puts it, “‘being’ and ‘participation’ name the same relational tie”

(2012, 72).

Finally, let us see again Prm. 158a3-6. This passage comes near the end of the third deduction’s first part. Parmenides has established that the others are one as a single whole, and he is now arguing that the others are one as parts. He says in the sentences immediately preceding this passage, “And the same reasoning applies to each part; for the part must partake of the One. For if each of the parts is a part, the word ‘each’ implies that it is one,

81 Some may doubt my construal of these lines, proposing that here Parmenides says only that “the others, if they are not many, then there is no sense in which they could be other than one.” Note: not the One.

Some additional support for my preferred construal might be found by reflecting briefly on the contrast between the others partaking of the One “in a certain way” (pê, 157c2) and the One’s being “altogether one.” When Aristotle asks Parmenides just what is this “certain way” in which the others partake of the One, what Parmenides tells him is that this “certain way” in the others’ having parts. It is the others’ having parts that makes them other, and not the One, for the One, as we are told at the outset of the first deduction (Prm. 137c-d), has no parts (nor, for that matter, is it a whole or many). These three attributes depend on each other, as the opening moves of the first deduction indicate. For instance, something without parts can neither be a whole nor many, as a “whole” is that from which no part is lacking, and something is “many” just in case it has parts (in some sense or other). But if something has no parts, is not a whole, and is not many, then it is altogether one. (This appears to be a “negative definition” of the One; see Prm. 137c4-d5) Put differently, something that lacks these three attributes would be the One. And this is precisely what I take Parmenides to be saying here.

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separated from the rest, and existing by itself; otherwise it will not be an ‘each’” (Prm.

157e6-158a3). Parmenides continues,

But it [each part] would partake of the One, while clearly being something other than

one. Otherwise, it wouldn’t partake, but would itself be one. But as it is, it is surely

impossible for anything except the One itself to be one. — Impossible. (Prm. 158a3-6)

We are told that each part partakes of the One, and is clearly other than one.82 Why this is the case is straightforward if we recall Prm. 137c4-d5. Parts are parts of a whole. But the

One is not a whole and has no parts, because the One is one and not many. If this were not the case — if the others were not other than the One, being neither a single whole nor having parts — then the others would be one. Just as with the phrase pantelôs an hen eiê at Prm.

157c4, so too should we understand ên … hen and heni … einai here as “be the One.” From which Parmenides concludes, it is impossible for anything except the one itself to be one — to be the One. While this passage tells us that the others, as parts, are one through their participation in the One, it does not tell us that the One is one (even though the One is one).

Moreover, and as with Prm. 157b8–c4, this passage does not tell us how the One is one, much less that it is in virtue of the One’s being the One that the One is one. Therefore, this passage too is not evidence for Gill’s claim that “‘being’ and ‘participation’ name the same relational tie” (2012, 72).

82 Recognition of this point goes a long way towards securing my desired conclusion. Why would Parmenides say that each part is “clearly other than one” if this did not mean “clearly not identical with the One”?

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J. Taking Stock

Let us take stock. Gill claims that in the Parmenides and the Sophist there is evidence that “‘being’ and ‘participation’ name the same relational tie” (2012, 72). As I understand this claim, it asserts that there are two possible explanations — “being” and “participation”

— for how some thing instantiates some quality, and which explanation applies in a particular case is determined by the subject in question. And it is a consequence of this that every Form is an instance of itself, since every Form is the Form that it is. My response is that none of the passages that Gill cites in fact support the claim that “‘being’ and

‘participation’ name the same relational tie” (2012, 72). The passage from the Sophist does not contain statements of self-instantiation. Rather, it contains statements about the natures of Largeness, Beauty, and (the parts of) Difference. And the pair of passages from the

Parmenides establish that the others are not identical with the One because the others have parts, while the One has no parts. Neither of them says anything about the One itself, nor how it is that the One is one, much less that it is in virtue of the One’s being one that the

One is one. I submit that there is no textual support for Gill’s claim that “‘being’ and

‘participation’ name the same relational tie” (2012, 72). Consequently, there is no reason to suppose that all Forms are instances of themselves. Therefore, my argument for the conclusion that self-participation is limited to certain Forms stands firm. Only some Forms participate in themselves because only some Forms are instances of themselves.

K. Forms, Dialectic, and Self-instantiation

Why is it the case that only some Forms are instances of themselves? My answer to this question is rather simple: the Forms must have certain “structuring features” to be Forms at all, the objects of knowledge, and graspable by reason. “Structuring features” include: being,

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oneness, sameness, difference, likeness, and unlikeness. If, say, Beauty is not or is not one, then it cannot be Beauty — what beauty is — one of the objects of knowledge, and graspable by reason. Beauty must partake of Being, Oneness, and other “structuring Forms,” as I will call them, if it is to be Beauty. But the Forms that are the cause of Beauty’s having these structuring features — Being, Oneness, Sameness, Difference, Likeness, and

Unlikeness — must themselves have these features. If Being was not or was not one, it would not be Being. Indeed, if Being was not or was not one, then there would be no other

Forms at all, as nothing would be. Recognition of this point helps us see that the world of the Forms depends on these structuring Forms.83 Yet these structuring Forms cannot support the entire world of the Forms unless they too are structured in the above ways. For this reason, each of them participates in all of the other structuring Forms, and also in itself, so that it is an instance of itself. Being must participate in Oneness, Sameness, Difference,

Likeness, and Unlikeness, so that it is one, the same, different, like, and unlike, and also itself, so that it is.

Not all Forms, though, play this structuring or supportive role. The Forms being Forms does not depend on their being large, small, or equal. In addition, the Forms are not Forms if they change, as the Forms are immutable. Since this is the case, Largeness, Smallness,

Equality, and Change are not instances of themselves.

83 If this is correct, then a natural question is, How does this relate to Socrates’s declaration at Rep. 508ef. that the world of Forms depends for its being on the Form of the Good, which is said to be “beyond being”? Has Plato changed his mind about the structure of the world of Forms? Or is there a way of reading the picture presented in the Republic, and that which we find in the Parmenides and the Sophist, in agreement with each other? These are important questions, and I plan to consider them at length elsewhere.

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I am well aware that this answer to our present question raises questions of its own, and I shall address two of them at the end of this chapter. For the moment, I want to show that my answer to the why question is to be found in the Parmenides and the Sophist. In addition, I suggest that this answer is Plato’s own — the Parmenides is not, as Vlastos famously put it,

“a record of honest perplexity” (1954, 343) — and that Plato challenges us, his readers, to arrive at it for ourselves.

L. Philosophy and the Philosopher’s Art

We begin with the Parmenides. Specifically, that portion of the dialogue that transitions us from its first part to its second part (Prm. 134e10-137c3). Parmenides has just shown that the Forms are wholly irrelevant to the perceptible world, unable to fulfill the roles that

Socrates intends for them. As a result, some many deny that there are Forms at all. Or, conceding that there are Forms, may maintain that it is not possible for them to be known by human beings. Parmenides asserts that either consequence is problematic. If the existence of the Forms is denied, or it is not possible for us to know them, then we will utterly destroy the art of dialectic (tên tou dialegesthai dunamin pantapasi diaphtherei, Prm. 135c1-2).

Should this happen, Parmenides asks Socrates, “what will become of philosophy? To what can you turn if these things [the Forms] are unknowable?” (ti oun poiêseis philosophias peri; têi trepsei agnooumenôn toutôn, Prm. 135c6-7). Socrates replies that he does not know, at least not at present.

Why would the non-existence or unknowability of the Forms destroy dialectic?

Moreover, why would this endanger philosophy itself? An answer to these questions is found in the Sophist. At Soph. 253b8 f., the Eleatic Stranger states that he and Theaetetus agree that the Kinds (ta genê) can mix (mixeôs) with each other, and in the same way as

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letters and musical notes (Soph. 252e10-253b7). It is not the case that every Form participates in every other Form, but every Form participates in some Forms, and there are some Forms in which all Forms participate.84 In addition, just as there is an art (technê) in the case of letters — the art of grammar — that is necessary for correctly combining the letters, so too

… if someone is going to show us correctly which Kinds harmonize (sumphônei)

with which and which do not receive (ou dechetai) each other, must he not possess some

science (epistêmê) as he proceeds through the discussion (tôn logôn poreuesthai)? In

addition, must he not know whether there are any Kinds that run through all of them and

link them together, making them capable of blending (summignusthai dunata einai), and

also, when there are divisions, whether certain Kinds running through wholes are always

the cause of the division? (Soph. 253b10-c4)

Theaetetus replies that he does need such a science, perhaps even the greatest science.

This science is none other than dialectic (tês dialektikês … epistêmês, Soph. 253d1-3), the division of Kinds by nature (eidos), and the avoidance of the belief that the same Kind is another or another the same. It is the science that belongs to free men (tôn eleutherôn, Soph.

253c8-9), those who pursue philosophy with purity and righteousness (tôi katharôs te kai dikaiôs, Soph. 253e6) — the philosophers themselves. Here is the Eleatic Stranger’s full description of the philosopher’s art,

If a person can do [this], he will be capable of distinguishing perfectly

(diaisthanetai) a single Form spread out all through a lot of other things, each standing

84 Nehamas (1982) 343. 131

separate from the others. In addition, he can distinguish perfectly Forms that are

different from each other, but are included within a single Form that is outside them, or a

single Form that is connected as a unit throughout many wholes, or many Forms that are

completely separate from others. That is what it is to know how to discriminate by Kinds

how things can associate and how they cannot. (Soph. 253d5-e3)

These descriptions of dialectic from the Eleatic Stranger undoubtedly raise many questions. For our purposes, though, we need only notice that the science or art of dialectic is the philosopher’s art; it is what it is to practice philosophy. In addition, the objects of dialectic just are the Forms, at times also called “Kinds.” The dialectician — the philosopher

— will know and be able to show why it is not the case that every Form participates in every

Form, but that every Form participates in some Forms, and which these are, and single out those Forms in which all Forms participate, and so on. But if there are no Forms, or if the

Forms are unknowable to human beings, then the art of dialectic either has no object or, if it does, it still cannot be practiced by us. It is a consequence of this philosophy itself is jeopardized. For philosophy, as the Eleatic Stranger’s remarks suggest, just is dialectic understood in this way.

Now notice what follows these descriptions of dialectic. From Soph. 254b10-258c7, the

Eleatic Stranger and Theaetetus practice dialectic. It is shown how the Great Kinds —

Being, Sameness, Difference, Rest, and Change — do and do not combine, and the nature of

Difference is analyzed in some detail.85 Parmenides had asserted that, as the young Socrates presented the Forms, their existence and knowability, and therefore philosophy itself, were

85 It remains an open question whether the Eleatic Stranger and Theaetetus are correctly practicing dialectic, as no Kind or Form partakes of Rest. But all Forms are at rest, are they not? I plan to pursue this question elsewhere.

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all in doubt. But here there are no such concerns. So, our question becomes, How are the

Forms now different? What has changed so that their existence and knowability are not in doubt, and that ensured the possibility of practicing philosophy?

M. The Phaedo, the Republic, and the Parmenides

We begin with the Forms in the Phaedo and the Republic. The Forms in these dialogues do not participate in each other. The reason for this seems to be the Forms’ status as ta onta.86 As Nehamas writes, “the capacity to participate seems to go along with the incapacity to be — and it is to that extent unlikely that that the Forms (pure, total, and real beings) should have the capacity or the need to participate in anything” (1982, 347).

This is also the case for the Forms as Socrates presents them in the first part of the

Parmenides. Consider the following,87

1. Socrates says at Prm. 130a1 that all of the Forms’ participants are sensible things

(horômena). Since the Forms are not sensible things, the Forms are not participants

(alternatively, they do not participate in each other).

2. Socrates accepts the conclusion of Zeno’s paradox (Prm. 127e1-128a1), but only up

to a point. He agrees with Zeno that the things-that-are (ta onta) cannot be qualified

in opposing ways (for example, like and unlike). However, Socrates contends that

only the Forms are rightly called ta onta, and maintains that it is only their

participants that are qualified in opposing ways. Indeed, the participants are so

86 For a defense of these claims, see Nehamas (1982) 343-45, 351-2.

87 What follows draws on the discussion in Nehamas (1982) 347-52.

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qualified precisely because they participate in the corresponding Forms. This

suggests that the Forms are not qualified in opposing ways because they do not

participate in each other.

3. Recall Socrates’s challenge to Parmenides and Zeno. He says, “... if someone first

distinguishes as separate the Forms, themselves by themselves, of the things I was

talking about a moment ago — for example, Likeness and Unlikeness, Multitude and

Oneness, Rest and Motion, and everything of that sort — and then shows that in

themselves they can mix together and separate (sugkerannusthai kai diakrinesthai), I

for my part,” he said, “would be utterly amazed, Zeno. I think these issues have been

handled with great vigor in your book; but I would, as I say, be much more

impressed if someone were able to display this same difficulty, which you and

Parmenides went through in the case of perceptible things, also similarly entwined in

multifarious ways in the Forms themselves — in things that are grasped by

reasoning” (Prm. 129d7-130a3).

As I pointed out in Chapter III, We can understand Socrates’s position in (3) in a weak or strong way. On the weak version, Socrates maintains only that any given Form is not qualified by its opposite. For instance, the One is not many, but it is still, say, both like and unlike. By contrast, the strong version understands Socrates as outright denying that the

Forms bear any quality other than their own. For instance, the One is only or simply one. As

I understand Socrates, he intends the strong version here, and I shall say something about why below. Understood in this strong way, Socrates’s challenge to Zeno and Parmenides indicates that he does not allow Forms to participate in other Forms. I submit that (1) – (3)

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indicate that, just as in the Phaedo and the Republic, the Forms do not participate in each other in the first part of the Parmenides.

It is clear that this is no longer the case in the Sophist. Once more, we learn in that dialogue that Forms can participate in other Forms. In addition, I have argued that we also learn that some Forms participate in themselves. We have also seen that this change is necessary for the Forms to be the objects of dialectic. If the Forms could not participate in each other, then the dialectician — the philosopher — would not be able to know or teach why it is not the case that every Form participates in every Form, but that every Form participates in some Forms, and which these are, and single out those Forms in which all

Forms participate, and so on.

But the reason for this change is not that the Forms must fit into a particular conception of dialectic, although this is a consequence of their being changed in this way. It is that, without allowing the Forms to participate in each other, there would be no Forms at all. And this brings us to the second part of the Parmenides.

N. Parmenides’s Demonstration and the Forms’ Purity

Parmenides’s demonstration, which spans the entirety of the dialogue’s second part, is peculiar in several ways. One of them is that while the third and fourth, fifth and sixth, and seventh and eighth deductions all derive positive conclusions, and then negative conclusions, respectively, the first and second deductions are different. The first deduction derives negative conclusions, while the second deduction derives positive conclusions; the order, whichever way you look at it, is reversed.

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Why is this the case? I wrote above that I understand Socrates’s challenge to Parmenides and Zeno (Prm. 129d7-130a3) in the strong way — Socrates outright denies that the Forms bear any quality other than their own. The One, for instance, is only or simply one, and the reason for this, I maintain, is that the Forms do not participate in each other. Without participating in, say, Likeness and Unlikeness, there is no way for the One to be like and unlike. So, it is neither like nor unlike, in addition to not being many. The One is just what it is in virtue of itself — one. I called this in Chapter III the “purity” of the Forms.

This contention that the Forms are “pure” explains why the first deduction derives entirely negative conclusions from its governing hypothesis, If the One is one.88 The One is not many because it is one. It is not a whole nor does it have parts, and for this reason is without a beginning, middle, and end, and so forth. In fact, it even explains why towards the deduction’s end Parmenides argues that the One is not, and so is not one (Prm. 141e9-

142a1). These conclusions are possible precisely because, as Socrates has presented them, the Forms do not participate in each other. The One does not participate in Being, and so is not. But if it is not, then it cannot be one (or anything else for that matter). These consequences can be avoided only if the One is structured in certain ways through it participation in other Forms. Minimally, it must participate in Being, so that it can be and be one.

It is no surprise, then, that the second deduction opens with an explicit acknowledgement of the One’s participation in Being (Prm. 142b6-7; 142c6-8), so that the One is and is one.

But notice this too: that once there is the One and Being, there is also Difference, which ensures that both the One and Being (and itself) are different from each other (Prm. 143b4-

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9). The introduction of participation in any one structuring Form necessarily brings along with it participation in other structuring Forms. For we are now speaking of two things — technically, three things — things that must be structured and related to each other in certain ways for them to be what they are at all.

The third and fourth deductions provide us with a different perspective on the importance of these structuring Forms. The third deduction (Prm. 157b7-159b2) presents the ways in which the others are one — both as a single whole and as parts of that whole. In addition, it reveals that the others are one in these ways through their participation in the

One. Considered solely by themselves — what they are in virtue of their own natures — the others are unlimited in multitude (Prm. 158b5-c9). It is only through their participation in the One that the others become structured in a certain way — that something arises in each of them that givens them limitation in relation to each other (Prm. 158d3-7) — so that each is an “each,” a “this,” or a “that.”

Then in the fourth deduction (Prm. 159b3-160b5), where the others are precluded from partaking in the One in any way, we see how the absence of the One’s structuring role compromises the others. Here the others are not at all one. But neither are the others many.

For their being many requires that each of them be one and part of a whole, which is not possible without participation in the One (Prm. 159d3-e1). The others are an indescribable

… something, and even this is not quite correct, as it suggests that there is some thing still present when the others are apart from the One. But, strictly speaking, there is not.

Parmenides goes on to show that without participation in the One the others cannot be like or unlike, same or different. The reason is simple: an essential structuring feature is missing

88 For a defense of this rendering of the hypothesis governing the first deduction, see Gill 137

from the others. We see that the others necessarily depend for their being others on their participation in the One and, though not highlighted by Parmenides, in Being. This tells us that, while collectively the structural Forms support the entire world of the Forms, Being and the One play a particularly important role. Without participation in either of them, and each of them in itself, no other structuring Form can do its job of providing the other structuring features. There is a sense, then, in which the entire world of the Forms depends on Being and the One.

Although this is just a sample of passages from Parmenides’s demonstration, I submit that they are sufficient for our purposes. If the Forms are not structured in certain ways, then there are no Forms at all. However, the Forms being structured in certain ways — being, being one, the same, different, like, and unlike — requires the Forms to bear qualities other than their own. Indeed, in some cases some Form must bear its own opposite. Sameness must be both same and different, Likeness must be both like and unlike, and so on. But this in turn requires that Forms participate in other Forms. If Socrates is to save the Forms from

Parmenides’s criticisms, and thereby save dialectic and philosophy itself, he must abandon the purity of the Forms.

Yet the Forms participating in each other, and importantly in the “structuring Forms,” is not sufficient to save them. The structuring Forms must also be structured in just those ways that other Forms are structured by participating in them. Without this, there are no structuring Forms to be participated in, and if this is the case then there is no world of Forms at all. But not all Forms play this structuring role, and therefore it is not necessary for them to be instances of themselves. Indeed, some of them should not be, as this would be

(2012) 57-61. 138

detrimental to the world of the Forms. Notable here is the Form of Change. Thus, Plato needs a way to limit the Forms that are instances of themselves. He cannot maintain that the

Forms are instances of themselves in virtue of their being the Forms that they are. Rather,

Plato must maintain that it is one thing for some Form to be the Form that it is, and another thing for that Form have its own character—to be an instance of itself. “Being” and

“Having,” if you will, must be kept distinct. For this reason, some other explanation is needed for self-instantiation, and this, as I have argued, is self-participation. Some Form is an instance of itself by participating in itself, just as other things are instances of that Form by participating in it. The Forms that participate in themselves, and so are instances of themselves, will be just those Forms that play this supportive or structuring role.

O. Conclusion

My answer to the why question — that only some Forms are instances of themselves because only some Forms serve a structuring or supportive role in the world of the Forms — raises questions of its own. This chapter closes by considering two of them. The first concerns the aesthetic and moral Forms, Beauty, Justice, the Good, and so on. The second focuses exclusively on the Form of Change.

The previous section’s language suggests that my position is that it is necessary for any

Form’s being an instance of itself that it serve a structuring role in the world of Forms.

Therefore, any Form that does not play this role cannot be an instance of itself. This includes not just Largeness, Smallness, and Equality, but also Beauty, Justice, and the Good. Some readers may agree that the former Forms are not instances of themselves, but maintain that

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the latter certainly do self-instantiate. And they may cite passages from the Phaedo, the

Republic, and the Symposium in support of their position.89

Suppose that these aesthetic and moral Forms are instances of themselves. How would this affect my answer to the why question? Should we outright reject it? No. If the aesthetic and moral Forms are in fact instances of themselves, then I can weaken my answer to the why question — it is a sufficient condition for self-instantiation that some Form serves a structuring role in the world of Forms. Weakening my answer in this way preserves the possibility that some Forms may be instances of themselves though they do not play this role; they are instances of themselves for some other reason.

If my answer to the why question is weakened in this way, though, then my case for self- participation being limited to certain Forms is similarly weakened. Recall that I argued that self-participation is limited to certain Forms because only some Forms are instances of themselves. Initially I supported this argument by suggesting that it is a category mistake to maintain that, say, Largeness is large, Smallness small, and Equality equal. In addition, the

Forms are immutable. Therefore, it is not the case that Change changes. I also considered and responded to a potential objection from Gill. But missing at the end that discussion was a sustained, positive case for only some Forms being instances of themselves. The sections that followed provided this, and it still does even if it is only a sufficient condition for self- instantiation that some Form plays a structuring role in the world of Forms. However, the possibility that some Forms are instances of themselves for some other reason is compatible with all Forms being instances of themselves. There could be one reason for the structuring

89 I am inclined to think that even if these Forms did self-instantiate in these dialogues, they no longer do following the Parmenides. Indeed, Plato does not seem to be interested in these Forms at all in the late dialogues. But I shall not press the point here. 140

Forms, another reason for the aesthetic and moral Forms, and yet another reason for another class of Forms, and so on.

I will not pursue this issue any further here. Let my outline of the available response, its effect on the main arguments of this chapter, and potential difficulties suffice for now.

Instead, I want to focus exclusively on the Form of Change.

Readers familiar with the Sophist will recognize that my argument, “The Forms are immutable. Therefore, it is not the case that Change is an instance of itself,” is by no means uncontroversial. There is a section of the dialogue often called “the Battle of Gods and

Giants” (Soph. 245e9-249d8). Here the Eleatic Stranger proposes a “mark” or a “definition”

(horos) of Being. He says,

I suggest that everything which possesses any power (dunamin) of any kind, either to

produce change (poiein) in anything of any nature or to be affected (pathein) even in the

least degree by the slightest cause, though it be on only one occasion, really is. For I set

up as a definition to define of Being, that it is nothing but power (dunamin). (Soph.

247d9-e4)

Towards the end of this section the Eleatic Stranger attempts to persuade the Gods, the

Friends of the Forms, to agree that the Forms are affected — they are changed — in coming to be known, and thereby accept his proposed mark or definition of Being. The Gods resist, maintaining that the Forms are immutable. The Eleatic Stranger does not press them on this point, but proceeds on with his discussion, eventually asserting that the philosopher must

“absolutely has to refuse to accept the claim that everything is at rest, either from defenders of the One or from friends of the many Forms. In addition, he has to refuse to listen to

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people who make Being change in every way. He has to be like a child praying for “both together” (xunamphotera), and say that that-which-is — everything — is both unchanging and having changed (akinêta kai kekinêmena)” (Soph. 249c10-d4).

The section raises many questions. For my purposes the important questions are, Should the Gods have accepted the Eleatic Stranger’s proposal, that the Forms are affected in coming to be known? Or are the Gods right to resist his argument, thereby retaining the

Forms’ immutability? How does the Eleatic Stranger’s description of the philosopher’s stance on Being affect our answers to these questions? Does Plato in this section signal that he no longer considers the Forms immutable? If the Gods should agree with the Eleatic

Stranger’s argument, if the Forms are no longer immutable, then it would seem that all

Forms must participate in the Form of Change, so that they can change in coming to be known. Moreover, Change must be an instance of itself, so that it too can be known.

Consequently, Change will participate in itself. The Form of Change will play a structuring role in the world of Forms.

It is an advantage of my answers to the how and why questions that they can accommodate whichever set of answers to the above questions ultimately proves correct. On the one hand, if the Gods are right to resist, then Change is not an instance of itself and so does not participate in itself. The reason for this is, as I have asserted several times now, that the Forms are immutable. Change does not play the requisite structural role to be an instance of itself; in fact, Change’s being an instance of itself would outright disqualify it as a Form.

On the other hand, if the Gods should concede the point to the Eleatic Stranger, then, again, all Forms would participate in the Form of Change, and Change in itself, so that all could be known. Indeed, it would now be the case that Change does play a structuring role in the

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world of the Forms. Without Change permeating the world of the Forms, they could not be the objects of dialectic and graspable by reason.

The latter possibility would significantly weaken my argument for self-participation being limited to certain Forms. In addition to the aesthetic and moral Forms perhaps being instances of themselves, if Change is also an instance of itself, then my case for only some

Forms being instances of themselves seems to rest entirely on Largeness, Smallness, and

Equality, and any other Forms for which it would be a category mistake to insist that they self-instantiate. This is not much nor very firm support for my argument.

The following chapter is concerned solely with this issue raised in the Eleatic Stranger’s and Theaetetus’s discussion of the Gods and the Giants. I shall show that the Gods are right to resist the Eleatic Stranger’s argument. The Forms are not changed in coming to be known.

No Form participates in the Form of Change, nor is Change an instance of itself.

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V. The Gods’ Resistance

A. Introduction

The previous chapter showed that it is not the case that all Forms are characterized by the very qualities they constitute, and therefore that it is not the case that all Forms participate in themselves. Put differently, I argued that self-participation, and so self- instantiation, is limited to certain Forms. My argument for these conclusions depends on the structuring role that some Forms play, while others do not, in the world of Forms. It is my position that playing a structuring role in the world of Forms is necessary for self- participation, and so self-instantiation. The present chapter is concerned with a question raised by this last claim.

The question concerns the Form of Change. It is simply this, Does the Form of Change play a structuring role in the world of Forms? It might be thought that the answer is an obvious, No. The Forms are immutable; they are stable, unchanging entities. However, there is a case to be made that the answer is in fact, Yes. If this is correct, then, given the position that I argued for in the previous chapter, the Form of Change would be characterized by the very quality it constitutes. The Form of Change would self-instantiate, it would be a changing thing.

The case for the latter answer centers on a passage from the Sophist, often called “the battle of Gods and Giants” (245-9).90 I shall refer to this passage simply as “the Battle.”

When the Eleatic Stranger and Theaetetus discuss the doctrines of the Gods, also called “the

90 All references are to the Sophist unless I indicate otherwise.

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friends of the Forms,” they focus chiefly on how it is that someone comes to know the

Forms. The Stranger proposes that knowing is a “doing” (poiêma), with the result that the

Forms are necessarily affected or changed (pathêma) when they come to be known. He asks,

Would the Gods accept this proposal? The answer is, No. The Gods outright reject it.

Despite the Gods’ resistance, though, many commentators maintain that the Stranger’s proposal remains alive, that it is a positive piece of Platonic doctrine, and for this reason must be incorporated into the theory of Forms. As a result, the Forms are no longer immutable; they are no longer stable, unchanging entities. This revision to the theory of

Forms results in the Form of Change plays a structuring role in the world of Forms. Since it is a necessary condition on some Form’s being an object of knowledge that it is affected or changed when it comes to be known, all Forms will participate in the Form of Change. But if this is the case, then the Form of Change will also participate in itself, and so be an instance of itself. The Form of Change (in fact, any Form at all) will be a changing thing.

Here I will argue that the Stranger’s proposal does not survive the Gods’ resistance. It is not a positive piece of Platonic doctrine, and for this reason should not be incorporated into the theory of Forms. As a result, the Forms on my view remain stable, unchanging entities.

Whatever revisions the theory of Forms undergoes following its critique in the Parmenides, it is not the case that the Forms lose their cherished immutability. It is also the case, by my argument, that the Form of Change does not play a structuring role in the world of Forms.

For this reason, the Form of Change does not participate in itself, and so does not self- instantiate.

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B. The Battle

The conflict between the Gods and the Giants concerns Being. Specifically, what kinds of things are beings. The Giants maintain that only what can be touched and handled

(prosbolên kai epaphên) is; they mark off (horizomenoi) Being as the same as body (sôma).

In addition, the beings of the Giants are different at different times, they are changing things.

The Gods, by contrast, say that true Being (tên alêthinên ousian) is certain intelligible, non- bodily Forms (noêta … asômata eidê). The Forms are always the same and in the same state; they are stable, unchanging entities. The Stranger’s aim in this section of the dialogue is in part showing that neither the Giants nor the Gods has the correct account of what kinds of things are beings. The correct account, the Stranger says, includes both. He tells Theaetetus at the Battle’s end that

[…] the philosopher — the person who values these things [knowledge, thought, and

intelligence] the most — absolutely has to refuse to accept the claim that everything is at

rest, either from defenders of the One or from friends of the many Forms. In addition, he

has to refuse to listen to people who make Being change in every way. He has to be like

a child praying for “both together” (xunamphotera), and say that that-which-is —

everything — is both unchanging and having changed (akinêta kai kekinêmena).

(249c10-d4)

I will refer to this account as “the Children’s Prayer.”

My concern in this and the following sections is how we should understand the

Children’s Prayer, as this determines whether the Forms retain their immutability, and therefore whether the Form of Change plays a structuring role in the world of Forms. There

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are two general interpretations. The first interpretation understands the Stranger as proposing only that the philosopher’s account of Being must capture both changing, bodily things as well as unchanging, non-bodily things.91 This interpretation maintains that the

Children’s Prayer is an account of what kinds of things constitute the realm of Being.92 The second interpretation disagrees, and says that there is more to the Children’s Prayer.

Specifically, by it bodily things must also be stable in some way or other, in addition to being changeable, while non-bodily things must also be subject to change in some way or other, in addition to being stable. There is disagreement in the secondary literature over just how bodily things should be stable and non-bodily things should be subject to change. But all proponents of this second interpretation agree that this additional requirement is warranted by the text. They claim that the Children’s Prayer is in fact an account of the nature of Being.93 It is a consequence of the second interpretation that the Form of Change plays a structuring role in the world of Forms. Since non-bodily things, in particular, the

Forms, are now subject to change in some way or other — no longer are they stable, unchanging entities — all Forms must participate in the Form of Change. As a result, the

Form of Change participates in itself, and so self-instantiates. It is a changing thing.

The choice between these interpretations turns on the fate of another account of Being that the Stranger introduces earlier in the Battle (247d8-e4). Specifically, whether this initial

91 We may contrast this with the Gods’ account of Being, which banishes the Giants’ bodily, changing things from the realm of Being, relegating them to the realm of Becoming (246b-c).

92 This is the minority position in the secondary literature. Supporters include Cornford (1935), Brown (1998), and Gerson (2005).

93 This is the majority position in the secondary literature. Supporters include Moravcsik (1962), Owen (1966), Friedländer (1969), Reeve (1985), and Gill (2012).

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account of Being survives an encounter with the Gods. If this initial account of Being does not survive, then the Children’s Prayer requires only that the realm of Being includes bodily, changing things as well as non-bodily, unchanging things. It is an account of what things constitute the realm of Being. If it does survive, though, then the Children’s Prayer requires that anything that is part of the realm of Being both changes and is at rest. It is in fact an account of the nature of Being.

Section C introduces the Stranger’s initial account of Being, which appears near the end of his and Theaetetus’s discussion of the Giants (247d-248a). I show that when introduced this account has a merely provisional status, that it is the subject of a dialectical agreement.

Then in Section D I turn to the Stranger’s and Theaetetus’s discussion of the Gods (248a3-

248e7). Although the Gods outright reject the Stranger's initial account of Being, some commentators maintain that it nevertheless survives the encounter. The reason is simple: there is a flaw in the Gods’ argument against it. I argue, however, that this is not the case —

I present a reading of the Gods’ argument against the Stranger’s initial account of Being that secures its dismissal. Section E concludes my engagement with the Battle. Some proponents of the second interpretation of the Children’s Prayer claim that the Battle’s final movement

(248e8-249c10) shows that the Stranger’s initial account of Being survives the Gods’ argument against it. I disagree, and argue that the Battle’s final movement in fact confirms that the account has been abandoned. Collectively, then, Sections D and E show that the

Stranger’s initial account of Being does not survive its encounter with the Gods. Therefore, the correct interpretation of the Children’s Prayer is the first interpretation. As a result, the

Form of Change does not play a structuring role in the world of Forms, and so is not (nor, for that matter, is any other Form) a changing thing.

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C. The Giants

The Stranger’s aim in the Battle is in part showing that neither the Giants nor the Gods has the correct account of what things constitute the realm of Being. The Giants maintain that Being is the same as body, which is tantamount to denying that any non-bodily things are. However, the Stranger compels them to admit some non-bodily things into their ontology. Consequently, the Giants abandon their materialism.

The Stranger accomplishes this in the following way: the Giants say that mortal animals

(or ensouled bodies) are among the things-that-are. So, the soul too is among the things-that- are. But souls are called either virtuous or vicious through the possession and presence

(hexei kai parousia) of various virtues and vices, respectively. So, the virtues and vices are also among the things-that-are. However, while the Giants say that the soul itself has a sort of body (sôma ti), they cannot bring themselves to say this about the virtues and vices. At the same time, though, the Giants are not willing to deny that there are virtues and vices.

The Stranger thus catches the Giants in a bind, which they escape by conceding that some non-bodily things (namely, virtues and vices) are. The Giants give up their materialism.

Some commentators wonder whether the Giants’ concession comes too quickly.94 The

Stoics would later maintain that the virtues and vices are bodies, for instance. I will not pursue this issue here, though, as my concern is with that which follows the Giants’ concession. With both bodily and non-bodily things now part of the realm of Being, the

Stranger says that the Giants must provide an account of what is common to them, because of which we say that both “are” and each “is.” That is, the Giants must provide an account

94 See, for instance, Brown (1998) 196-7.

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of the nature of Being. Since the Giants may find themselves at a loss (aporoien), the

Stranger offers the following on their behalf. He says

I am saying that a thing really is if it has any capacity (dunamin) at all, either by

nature to do something (poiein) to something else or to have even the smallest thing

done (pathein ... smikrotaton) to it by even the most trivial thing (phaulotatou), even if it

only happens once. I set up as a definition to define (horon horizein) the things-that-are

(ta onta) as nothing other than capacity (dunamis).95 (247d8-e4)

This is the Stranger’s initial account of Being, and I will call it “the dunamis proposal.”

The dunamis proposal says that anything that is just is capacity, which means that anything that is can either do something to another thing or have something done to it by another thing. It is not the case that whatever is must be capable of both “doing” and “being affected”; considered individually neither capacity is necessary for something to be. But anything that is must be capable of one of them — some things may very well be capable of both — and insofar as it is, that by itself is sufficient for the being of that thing.

I will turn to considering the proposal’s fate in a moment, whether it ultimately stands as an account of the nature of Being. But first, let us see how the Stranger and Theaetetus conclude their discussion of the Giants. This will assist us in determining the fate of the dunamis proposal in the Sections that follow.

Theaetetus says that the Giants accept the Stranger’s proposal, since they have nothing better to offer at present. Then the Stranger responds, “Good — perhaps later something else

95 The construction of this last sentence is difficult, as Cornford (1935) 234 n. 1 rightly points out.

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may appear to us and them. With respect to us and them, then, this is agreed upon and settled” (247e7-248a1). He, in my view, states that the dunamis proposal is a merely provisional account of Being.

This is confirmed once we notice the Stranger’s language leading up to, and included in, the response. The Stranger, after compelling the them to abandon their materialism, says that the Giants must provide an account of the nature of Being, something that captures both bodily and non-bodily things. He offers a suggestion (proteinomenôn hêmôn, 247d5), stating explicitly that his intent is securing an agreement (etheloien an dechesthai kai homologein,

247d6) about what Being is. And though the Stranger admits that the proposal may be replaced later, he nevertheless asserts that it suffices for securing the desired agreement between himself, Theaetetus, and the Giants (xunomologêthen, 248a1) concerning the nature of Being.

The use of homologeô here is particularly important, as it indicates that the agreement that the Stranger aims to secure is a dialectical agreement. Such agreements neither require nor imply a commitment from their parties concerning the truth of that which is agreed upon. Instead, they arise simply for the sake of the argument, and ensure that the conversation continues. Since this is the case, there is no reason at this stage of the discussion to regard the dunamis proposal as anything more than a merely provisional account of what Being is, and certainly not a positive piece of Platonic doctrine that should be incorporated into the theory of Forms.

This point constitutes an important step in my argument for the first interpretation of the

Children’s Prayer. Since the dunamis proposal has at its introduction a merely provisional status, proponents of the second interpretation must show that this changes at some later

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point in the conversation. Specifically, they must show that the proposal becomes a positive piece of Platonic doctrine. Otherwise, there is no reason to suppose that Children’s Prayer requires anything more than that the philosopher’s account of Being capture changing, bodily things as well as unchanging, non-bodily things; that it is an account of what things constitute the realm of Being.

D. The Gods

The Gods were introduced as those who maintain that what-truly-is is certain intelligible, non-bodily Forms. The changing, bodily things of the Giants they banish from the realm of

Being, relegating them to the realm of Becoming. At 248a, the Stranger says a few more things about the Gods’ position. Specifically, the Gods say that Being (ousia) and Becoming

(genesis) are separate (chôris); that Being is always the same and in the same state, but

Becoming is different at different times; and that we associate (or commune, koinonein) with Being with our souls, through reasoning (logismos), while we associate with Becoming with our bodies, through perception.

With the Gods’ views on Being and Becoming set forth, the Stranger turns to showing that the Gods too are mistaken about what kinds of things constitute the realm of Being. He begins by focusing on the Gods’ claim that we associate with the realm of Being by way of our souls, through reasoning, and with the realm of Becoming by way of our bodies, through perception. He is interested in just what the Gods mean by “associate” here. The verb koinonein in the late dialogues often signifies the participation relation, and is frequently

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used alongside the familiar verbs metechein and metalambanein.96 But this is not its meaning here — the Stranger is not inquiring how it is that we, with our souls and through reasoning, participate in the Forms.

Consider what follows. The Stranger proposes an account of association that incorporates the dunamis proposal.97 He says

Does it [associate] not mean what we said just now? … What happens when two

things come together, and by some capacity one does something to the other or has

something done to it? (248b3-7)

The Gods’ reply is, No. While things in the realm of Becoming share in the capacities of

“doing” and “being affected” — this account is applicable to them — neither of these capacities is fitting for the realm of Being. Theaetetus wants to know if there is something to this reply from the Gods. The Stranger himself says that he and Theaetetus must learn more clearly (saphesteron) if the Gods agree (prosomologousi) that the soul knows and that Being is known (tên men psuchên gignôskein, tên d’ ousian gignôskesthai, 248d1-3; cf. 248a10-3).

This response is important. Here the verb koinonein is replaced by, but treated as synonymous with, the verb gignôskein. This tells us, as I wrote above, that the Stranger’s interest is not the participation relation. The Stranger is inquiring into how it is that we, with

96 The entire section on the Great Kinds (254-9) is just one piece of evidence for this. Especially 256a-b, where all three verbs or their cognates are present and used interchangeably without any apparent difference in meaning.

97 This is the fifth account (of some sort or other) present in the Battle. However, it is not concerned with either what things are part of the realm of Being (as are the Giants’ materialism, the Gods’ immaterialism, and, as I am arguing, the Children’s Prayer) or the nature of Being (as is the dunamis proposal). As I explain below, its offers an account of how it is that we, with our souls and through reasoning, come to know the things-that-are.

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our souls and through reasoning, come to know the Forms. His concern is an epistemological one. In addition, notice that at this point in the conversation it is not clear to the Stranger and

Theaetetus why the Gods reject the Stranger’s account of association that incorporates the dunamis proposal.

The Gods do not reject the Stranger’s account because they have abandoned their position that Being is known by the soul through reasoning.98 So, the Stranger considers another reason. Focusing on his proposed account of association, he asks whether the Gods would say that “knowing” and “being known” are both “doings” (poiêma) or “having something done to itself” (pathêma), or if one is a “doing” and the other a “having something done to itself,” or if neither is a case of either. At first glance, this move by the

Stranger is odd. For remember that only a moment ago, the Gods said explicitly that “neither capacity is connected with Being” (ousian ... oudeterou tên dunamin harmottein, 248c10).

Recall, though, that the Stranger and Theaetetus are still in search of the Gods’ reasons for rejecting the proposed account of association.

When Theaetetus says that the reason for the Gods’ answer — that “neither is a case of either” — is that they would otherwise contradict themselves, the Stranger offers the following

I understand. You mean that, if knowing is doing something (poiein ti), then

necessarily (anagkaion) what is known has something done to it (paschein). When Being

is known by intelligence (hupo tês gnôseôs), according to this account, then insofar as it

98 See Theaetetus’s remark at 248d4.

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is known it is changed by having something done to it (kineisthai dia to paschein) —

which we say would not happen to something that is at rest (to êremoun). (248d11-e6)

This is why the Gods’ reject the Stranger’s account of association that incorporates the dunamis proposal. It is the Gods’ position that Being is always the same and in the same state (248a12; here, Being is at rest), while the Stranger’s account requires that Being is subject to change. The Gods will not accept the latter, they refuse to give up the cherished immutability of the Forms. This is the Gods’ resistance.

This argument from the Stranger raises some questions. Brown, for instance, wonders whether it in fact establishes that, with respect to knowing and being known, “neither is a case of either.” She points out that the Stranger presents the Gods with six possibilities,

1. Knowing and being known are both “doing”

2. Knowing and being known are both “having something done to itself”

3. Knowing and being known are both “doings” and “having something done to itself”

4. Knowing is a “doing” and being known “having something done to itself”

5. Knowing is “having something done to itself” and being known is a “doing”

6. Neither is a case of either

The argument rules out (1) and (2), she writes, “[as] it is taken for granted that if one of the two is a poiêma, the other must be a pathêma” (1998, 196). It also rejects (3) and (4), as these possibilities require that Being is subject to change, which contradicts the Gods’ position that Being is always the same and in the same state. But (5), Brown claims, “is left untouched by the argument” (1998, 196).

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This possibility demands my attention. If Brown is right, then the dunamis proposal — and in fact the Stranger’s account of association that incorporates it — may very well survive its encounter with the Gods. This would prepare the grounds for a further argument that it is in fact a positive piece of Platonic doctrine, and therefore must be incorporated into the theory of Forms. But my position is that this is not the case, that the dunamis proposal is dropped from the conversation, and that this confirms the first interpretation of the

Children’s Prayer.

Why does Brown claim that (5) is not touched by the argument? She reminds us that the reason for the Gods’ resistance is that being is always the same and in the same state

(248a12). While the accepting (3) or (4) would violate this requirement, she says that accepting (5) does not. The Forms can have the power to affect, but remain immune from being affected (1998, 199).99 For support, Brown draws our attention to a famous passage in the Phaedo (100d5) where it is claimed that “nothing else makes (poiei) a thing beautiful but the presence in it of the beautiful. So Forms are naturally thought of as capable of poiein”

(1998, 199).

I am not convinced. First, as I have been arguing throughout the dissertation, the theory of Forms undergoes substantial changes following its critique in the Parmenides. So, while the Forms in the Phaedo may very well have been thought capable of “doings” (or poiein) this by itself is no guarantee that they are still conceived of in this way following

Parmenides’s critique.100

99 This possibility is also considered by Cornford (1935) and Ostenfeld (1982).

100 However, Brown (1998) 199 n. 35, does direct our attention to 247a, where “the existence of justice has been established by observing that it can come to be present in someone’s soul, and thereby, one assumes, affect it; hence the dunamis proposal is intended 156

Second, recall that when the Gods are asked whether they would accept the Stranger’s account of association, their answer is that while Becoming shares in the capacities of doing and being affected, neither capacity is connected with Being (248c8-11). The Gods are said

— twice, in fact — to reject both capacities as fitting for the realm of Being (248c11, 248d9-

10). It is, of course, possible that the Gods are mistaken about this. But the Stranger never indicates anything of the sort, nor does Theaetetus. Indeed, both of them agree (manthanô,

248d11; orthôs, 248e7) that, because the Gods hold that Being is always the same and in the same state, (6) follows from the Stranger’s argument.

I want to now offer an interpretation of the argument on which the Gods do secure their stated conclusion, and where the Stranger’s and Theaetetus’s assessment of the argument is correct.

Let us begin by revisiting Brown’s claim that the argument presented by the Stranger rules out (1) – (4), and that (5) is left untouched. This is not the case. The argument rules out only (4). The reason for this is straightforward: the argument is a reductio ad absurdum.

When the Stranger assumes (eiper, 248e1) at the outset that knowing is a “doing,” so that necessarily being known is “having something done,” it is this possibility alone that is targeted, and then rejected, by the line of reasoning that follows. The mere rejection of (4) does not affect possibilities (1) – (3) and (5).

It might seem that this interim conclusion runs counter to my general endeavor.

However, this is not so. Although the Stranger presents this argument on behalf of the Gods

to include as being such things as justice, despite their incorporeality. But we cannot be sure that these are intended to be Forms.”

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only once, it is intended to be repeated for possibilities (1) – (3) and (5). These repeated applications of the argument, taken together, justify the Gods’ assertion of (6).

Consider possibilities (2) and (3), by which being known is (either in whole or in part)

“having something done.” These possibilities are dismissed for the very same reason that led to the rejection of (4). By them, too, is Being subject to change, but the Gods maintain that

Being is always the same and in the same state.

What about possibilities (1) and (5)? I shall deal with only (5) directly, as if it is ruled out by the argument, then so too is (1). This possibility conceives of the Forms as active entities. And this, I claim, requires that Being is subject to change just as much as does (4).

Consider this case. As I am sitting here, writing this paragraph, I do not know the Form of

Justice. But suppose that tomorrow, after engaging in dialectic over coffee with a colleague,

I miraculously come to know the Form of Justice. If knowing is “having something done” and being known is a “doing,” then has not the Form of Justice undergone a change here? It would seem that it has. The Form of Justice was previously not affecting me, and as a result

I did not know it. But on the following day this changed; as a result of my efforts, the Form of Justice now is affecting me, and as a result I do know it. It is in a different state, and this runs afoul of the Gods’ view that Being is always the same and in the same state. Thus, on

(5) too — and a fortiori (1) — the Forms do not remain stable, unchanging entities.101

101 I suspect that Gill would be receptive to this line of reasoning, for she argues that Plato is committed to the view that “a change in the changed counts as a change of the changer as well, even though the changer undergoes no alteration of its own properties in the encounter” (2012, 236; emphasis in the original). I will not review Gill’s argument for this position here, though, as it weaves together the account of change and rest in the Timaeus with Aristotle’s definition of change. Consideration of these issues would take us too far afield from the Battle.

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It will not do to say, in response to this case, “Fair enough. But the Form of Justice has not changed with respect to its essential properties or its nature. It is only its accidental properties that changed when it began to affect you, as a result of your efforts, and because of which you came to know it. Therefore, the Form of Justice did not really change when it came to affect you. It remains immutable in this way.”102 The reason that this is not a tenable response is that when the Stranger presents the Gods’ views on Being and Becoming, there is no distinction drawn in the text between essential properties and accidental properties, much less is it said anywhere in the Battle that a change in the latter does not violate this tenet of the Gods’ position. All that is said is that Being is always the same and in the same state. What the text requires, I submit, is that we understand this claim in the most general way, in a way that rules out any change at all for the Forms.

My interpretation, then, is this: the Stranger presents an argument on behalf of the Gods that focuses exclusively on possibility (4), but is intended to be repeated for possibilities (1)

– (3) and (5). The reductio is identical in each case — whichever possibility is assumed requires that Being is subject to change, but the Gods maintain that Being is always the same and in the same state. For possibilities (2) – (4), their rejection is straightforward. But for possibility (5), and also (1), it requires appreciating that the Forms, when conceived of as active entities, must also be subject to change. Still, the conflict is the same between the

Stranger’s account of association and the Gods’ views on Being. The result is that the Gods are in fact justified in asserting (6), that with respect to knowing and being known “neither is a case of either.”

102 It may very well be the case that Plato (or the Gods, if you prefer) should say something along these lines, as suggested by Keyt (1969). But the fact of the matter is that this sort of response is not justified by the text, and that is all I am concerned to argue for here.

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It is a further consequence of my interpretation that the Stranger’s and Theaetetus’s assessment of the argument is correct. It would be one thing to say, as Brown does, that the argument as stated in the text rules out possibilities (1) – (4), leaving (5) untouched. The

Stranger’s and Theaetetus’s assessment is ultimately incorrect on her interpretation. But it could be said that “this is a clue that Plato has left for the careful reader.” However, once it is appreciated that the Stranger’s argument as stated in the text rules out only possibility (4), there is no plausibility in this appeal to “detective work.” The Stranger and Theaetetus would not be overlooking a single possibility. Instead, they would overlook four of the six possibilities that are presented to the Gods (248d5-8); they would be grossly in error about the success of this argument. The very intelligibility of the Stranger’s and Theaetetus’s discussion here, I conclude, requires my interpretation.

The upshot of these results is that the Stranger’s argument on behalf of the Gods’ resistance does not leave open the possibility that the dunamis proposal is still in play.

Consequently, it cannot serve as the foundation for a further argument that the proposal is a positive piece of Platonic doctrine that must be incorporated into the theory of Forms, which would result in the Forms losing their cherished immutability, with the joint result that the

Form of Change would play a structuring role in the world of Forms.

The section that follows consider another reason for supposing that the dunamis proposal survives its encounter with the Gods. But this reason too cannot withstand scrutiny. What emerges is an alternative reading of the Battle’s closing movement on which the dunamis proposal is dropped from the conversation at the moment of the Gods’ resistance.

Collectively, these conclusions confirm the first interpretation of the Children’s Prayer.

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E. The Stranger and Theaetetus

So far as I can tell, every commentator maintains that the Stranger’s and Theaetetus’s engagement with the Gods does not end at 248e7, where Theaetetus says in response to the argument discussed in the previous Section, “Right.” Rather, it continues down to 249e9, after which the Stranger introduces the Children’s Prayer, which brings us to the Battle’s end. Every commentator maintains, that is, that the Battle has a bipartite structure.

This is wrong. Up to 248e7 Theaetetus, who has been predominately speaking on behalf of the Giants and the Gods, with the Stranger himself at times serving in this role for the latter, has almost always answered the Stranger’s questions in the third-person plural (“they say ...,” “they agree ...,” etc.). What is more, the Stranger has consistently put his questions to Theaetetus in the same way (“do they say that ...,” “would they agree that ...,” etc.). But this changes after 248e7. Questions are now put to Theaetetus in the first-person plural, and he responds in kind (“should we agree that ...,” “how can we say that ...,” etc.). The focus of the discussion from 248e7 onward is no longer the Gods. It is the Stranger and Theaetetus themselves. The Battle, I claim, has a tripartite structure, and recognition of this point is essential for correctly understanding this final part. Or so I shall now show.

The Stranger attempted to show that the Gods too do not possess the correct account of what things constitute the realm of Being. Central to his effort was the dunamis proposal and the Gods’ claim that it is with our souls, through reasoning, that we commune with the things-that-are. If the Gods had accepted the Stranger’s account of communion, then it would no longer be the case that Being is always the same and in the same state. This, in turn, would prepare the way for changing, bodily things to enter the realm of Being, just as the Stranger’s engagement with the Giants prepared the way for unchanging, non-bodily

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things to enter the realm of Being (as the Giants conceived of it). But the Stranger’s efforts met with resistance from the Gods. This means that, while the Stranger succeeded in securing a concession about Being from the Giants, he has failed to secure a similar concession from the Gods.

Although the Gods do not concede that changing, bodily things are part of the realm of

Being, the question remains whether the Stranger and Theaetetus should themselves should be persuaded (peisthêsometha, 248e9) by this. At the core of the Gods’ resistance is the claim that Being is always the same and in the same state. So, it is this that the Stranger sets his sights on. The ensuing arguments show that he and Theaetetus should not side with the

Gods, that they should not accept the claim that Being is always the same and in the same state. But recognition of this point does not result in a revival of the dunamis proposal. It never reenters the conversation.

The Stranger asks Theaetetus whether they should be persuaded by the Gods that motion, life, soul, and thought are not present to absolute Being — that is, are not part of the realm of Being — that it neither lives nor thinks but, solemn and holy, is without intelligence, fixed, and changeless. Theaetetus replies that this would be a frightening admission,103 which prompts the Stranger to fashion another reductio ad absurdum (note the aloga at 249b1). He reasons that where there is intelligence, there is life; where there is intelligence and life, there is a soul in which these things are; and where there is intelligence and life in a soul, there are change and changing things. For it is not possible that something

103 Some readers may be interested in the Greek text at 248e8-249a2. It reads: Τί δὲ πρὸς Διός; ὡς ἀληθῶς κίνησιν καὶ ζωὴν καὶ ψυχὴν καὶ φρόνησιν ἦ ῥᾳδίως πεισθησόµεθα τῷ παντελῶς ὄντι µὴ παρεῖναι, µηδὲ ζῆν αὐτὸ µηδὲ φρονεῖν, ἀλλὰ σεµνὸν καὶ ἅγιον, νοῦν οὐκ ἔχον, ἀκίνητον ἑστὸς εἶναι; — Δεινὸν µέντ᾽ ἄν, ὦ ξένε, λόγον συγχωροῖµεν.

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with intelligence and life in a soul is also at rest and completely changeless (249a5-13).

From this the Eleatic Stranger concludes, “it must be conceded that that-which-changes and change are” (249b2-3) — that is, part of the realm of Being — for “if no beings change then nothing anywhere possesses any intelligence about anything” (249b5-7; see also 249c6-8).

The argument implicitly assumes that there is (or, at least that it is possible for there to be) intelligence about some things.

It is worth pausing for a moment to appreciate some aspects of this argument. The

Stranger’s concern is now metaphysical, no longer epistemological. Specifically, his focus is intelligence (nous), with the conditions necessary for there being any intelligence at all about anything. The Gods’ views on Being entail that there is no intelligence in the realm of

Being, much less intelligence of the beings themselves. The reason is that intelligence depends on (or requires) a living, ensouled body, which in turn requires change, as it is a changing thing. But these latter were banished from the realm of Being by the Gods, and along with them soul and life, and so intelligence too. Consequently, if there is to be intelligence at all about anything, then change and changing things must be part of the realm of Being. This argument, in effect, shows that the Stranger and Theaetetus should not be persuaded — indeed, that they cannot accept the claim — that Being is always the same and in the same state.

There is a further implication of this argument that is easily overlooked. Namely, that if there is to be intelligence about anything at all, the Stranger and Theaetetus must also reject the Gods’ position that the realms of Being and Becoming are distinct (246b9-c1, 248a7-8; cf. 248a10-3). The realm of Becoming, as the Gods conceive of it, just is the realm of change, the realm that the Giants’ changing, bodily things occupy. But if change and

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changing things must be part of the realm of Being for there to be any intelligence about anything, then, in elevating change and changing things into the realm of Being, nothing remains in the realm of Becoming. There is only the realm of Being, which now includes changing, bodily things, as well as unchanging, non-bodily things.

We should ask at this point if there are any additional implications of the Stranger’s argument for the position that he and Theaetetus are presently developing for themselves.

Specifically, whether the dunamis proposal might find its way into this nascent account of

Being, now that the reason for its rejection has itself been relinquished. What the Stranger says next tells us that the answer to this question is, No.

While change and changing things must be part of the realm of Being, which requires that it is not the case that Being is always the same and in the same state, the Stranger says that “if we were to admit that everything is moving and changing (pheromena kai kinoumena pant’ einai), then on this account we will take away the same thing (tauton touto) from the-things-that-are” (249b8-10). The phrase tauton touto here refers to

“intelligence” (nous); the Stranger’s claim is that if everything is moving and changing, which we might suppose is a further consequence of the previous argument, then intelligence is still not to be found anywhere about anything at all.

The line of reasoning that show this is as follows: suppose that everything is moving and changing. This means that nothing is at rest, and without rest, nothing is the same — nothing is in the same state and in the same respects. But intelligence requires, says the Stranger, that there are things that are the same, that are at rest (249b12-c5). Therefore, if everything is moving and changing, then it is not possible (note Theaetetus’s oudamôs at 249c2) for intelligence either to be or come-to-be (onta ê genomenon). The Stranger concludes, “we

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need to use every argument we can to fight against anyone who does away with knowledge

(epistêmên), thought (phronêsin), and intelligence (noun), but at the same time asserts anything at all about anything” (249c6-8). As with the previous argument, this argument too implicitly assumes that there is (or, at least that it is possible for there to be) intelligence

(alternatively, knowledge and thought) about some things.

This pair of arguments from the Stranger together establish two necessary conditions for the being or coming-to-be of intelligence. On the side of that which has intelligence

(alternatively, on the side of the knower), which is the focus of the first argument, there must be change, as intelligence requires life; life requires soul; and living, ensouled bodies require change, as they are changing things. On the other side, that of the objects of intelligence

(alternatively, of the objects of knowledge), which is the focus of the second argument, there must be sameness or rest. For the being or coming-to-be of intelligence also requires that there are things that are in the same state and the same respects.

Recognition of this last point is crucial to my general argument. We saw above that the dunamis proposal, a proposal about the nature of Being, requires that anything that is is subject to change. This is the case regardless of whether its capacity is affecting other things, being affected by other things, or both.104 And though the Stranger and Theaetetus found that they cannot accept the claim that Being is always the same and in the same state, a restricted version of this claim has just been shown necessary for the being or coming-to-be of intelligence: the objects of intelligence must be the same, they must be in the same state and in the same respects. Since the dunamis proposal directly contradicts this requirement, it cannot reenter the conversation, much less can it find a place in the Stranger's and

104 See my discussion of the Stranger’s initial argument above.

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Theaetetus's nascent account of Being. I conclude, therefore, that the proposal has in fact been abandoned as an account of the nature of Being. It was dropped from the conversation at the moment of the Gods’ resistance.

The Stranger has accomplished his aim — he has shown that neither the Gods nor the

Giants has the correct account of what things are beings. The Giants were compelled to admit non-bodily things into their ontology, since they say that there are virtues and vices, but would not say that these are bodily things. The Gods resisted the Stranger's proposed account of communion; a similar concession was not secured from them. However, the

Stranger went on to show that the Gods too do not possess the correct account of the things- that-are. Changing, bodily things must be elevated into the realm of Being, because it is a necessary condition on the being or coming-to-be of intelligence that change and changing things are. The result is that the realm of Becoming is no more. There is only the realm of

Being, which now includes changing, bodily things, as well as unchanging, non-bodily things. With this we are brought to the Battle’s end, where the Stranger introduces the

Children’s Prayer. For the sake of convenience, here it is once more. The Stranger says that

[…] the philosopher — the person who values these things [knowledge, thought, and

intelligence] the most — absolutely has to refuse to accept the claim that everything is at

rest, either from defenders of the One or from friends of the many Forms. In addition, he

has to refuse to listen to people who make Being change in every way. He has to be like

a child praying for “both together” (xunamphotera), and say that that-which-is —

everything — is both unchanging and having changed (akinêta kai kekinêmena).

(249c10-d4)

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I wrote in Section B that there are two general interpretations of this account of Being.

One interpretation understands the Children’s Prayer as only concerned with what things constitute the realm of Being. The Stranger, on this view, asserts only that the philosopher’s account of Being must capture both changing, bodily things and unchanging, non-bodily things. The other interpretation maintains that there is an additional requirement, because the

Children’s Prayer is an account of the nature of Being. By it, changing, bodily things must also be stable in some way or other, while unchanging, non-bodily things must also be subject to change in some way or other. The choice between these interpretations, I claimed, turns on the fate of the dunamis proposal. If it does not survive the Gods’ resistance, then this confirms the first interpretation. If the proposal does survive, though, this confirms the second interpretation.

My efforts in this section have been directed at supporting the first interpretation of the

Children’s Prayer. I considered one reason for supposing that the dunamis proposal survived the Gods’ resistance in the previous section, ultimately rejecting it. This section has so far been concerned to present an interpretation of the Battle’s final movement that confirms that the dunamis proposal was dropped from the conversation at the moment of the Gods’ resistance and abandoned as an account of Being, never to reenter the conversation. If my battery of arguments up to this point are sound, then I tentatively conclude that the

Children’s Prayer is concerned only with what things constitute the realm of Being. It says nothing about the nature of Being, save that, whatever the account of that is, it must capture both changing, bodily things and unchanging, non-bodily things.

It is a further consequence of this that, so far as concerns the Battle, there is no reason to suppose that the Form of Change plays a structuring role in the world of Forms. Since the

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Forms do not lose their cherished immutability — they remain stable, unchanging entities — no Form will participate in the Form of Change. Consequently, the Form of Change does not participate in itself, and so is not an instance of itself. It is not (nor is any other Form, for that matter) a changing thing.

These claims and conclusions remain tentative for the moment, though, as there is another reading of the Battle’s final movement that requires consideration. This reading comes from Gill, a proponent of the second interpretation of the Children’s Prayer, and for whom the Form of Change does play a structuring role in the world of Forms. It is a consequence of her view that the Form of Change (indeed, each and every Form) is a changing thing. The remainder of this section will show that Gill’s reading of the Battle’s final movement is not defensible. The result is that the above conclusions are no longer tentative; there is confirmation of the first interpretation of the Children’s Prayer.

Gill’s alternative reading depends on three claims. First, that the focus of the Battle is in fact the nature of Being, not merely with which kinds of things are beings. Second, that the

Stranger’s final arguments establish that the objects of intelligence must be both changeable as well as stable. Consequently, the Children’s Prayer is a “refinement” of the dunamis proposal (2012, 99), and so an account of the nature of Being. Third, after introducing the

Children’s Prayer, the Stranger claims to have captured Being in a logos, which Gill translates as “definition” (2012, 99).

The last claim, taken on its own, is not persuasive. The word logos can just as well be translated as “account” here. And this, together with the reading that I advanced above, would mean that the Children’s Prayer is an account of what kinds of things are beings. I

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draw attention to this possibility not because Gill intends for the third claim to be persuasive on its own, but because it focuses our attention on the first and second claims.

The first claim is simply false. It is true that an account of the nature of Being, the dunamis proposal, does appear in the Battle. So, it is not the case that concern with what

Being itself is is not found here at all. But the proposal is introduced as a provisional account of Being, the subject of a dialectical agreement, as I argued above, and at no point is it elevated to the status of a positive piece of Platonic doctrine. Instead, it is eventually dropped as an account of Being. Not only do the Gods reject it, the Stranger too, in piecing together with Theaetetus their own account of Being, forcefully and unqualifiedly reasserts the immutability of the objects of intelligence near the Battle’s end. It is a mistake, therefore, to maintain that the dunamis proposal’s brief presence in the Battle determines what the Battle’s principal concern is.

In addition, if we want to learn what the principal concern of the Battle is, we need only look at those passages that introduce it. When the discussion of Being is introduced, itself part of a larger discussion, namely, the refutation of Parmenides (241d-242b), we are told that the examination will come in two parts (242c5-8, and note the posa te kai poia at c7).

First, how many being there are. This is the discussion of Pluralism and Monism that preceeds the Battle (243-5). Second, what kinds of things are beings — the Battle itself.

It might be said that the sense of poia at 242c7 is “what Being is,” but the Stranger’s introduction of the disagreement between the Gods and the Giants rules out this possibility.

The Giants say that only bodily things are, outright rejecting the view that anything non- bodily is. The Gods, by contrast, say that only what is non-bodily truly is, and that the

Giants’ bodily things are part of the realm of Becoming. The disagreement between them

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concerns what kinds of things are Beings, not what Being itself is. And these issues are distinct. If I tell you that only bodily things are, only non-bodily things are, or that both bodily and non-bodily things are, I have not told you anything about why they are, about what is common to all bodily or non-bodily things (or both), and because of which all “are” and each individually “is.” So much, then, for Gill’s first claim.

These arguments may be resisted by advancing an alternative reading of the Stranger’s final argument (249b8-249c9). This brings us to Gill’s second claim. After the Stranger shows that change and changing things must be part of the realm of Being, Gill claims that the final argument targets the Giants. She writes that at this point, “[...] the Stranger turns back once more to the Giants, and claims that their view, according to which everything is changing, also eliminates reason from the realm of being [...] [t]he Giants and their kinsmen the Heracliteans go too far in rejecting rest (stasis) because without rest there would be no stable objects for reason to grasp” (2012, 97). The result is that “the Stranger tries to convince the Gods that the things they accept as real must be changeable as well as stable, since we can know them, [so too does he inform] the Giants that they must concede that things are stable, as well as changeable, on the same ground, since we can know them”

(2012, 97).

As I wrote above, the target of the Stranger’s final arguments is neither the Gods nor the

Giants, but the Stranger and Theaetetus themselves. This third movement of the Battle has as its central question, Should we — the Stranger and Theaetetus — join the Gods’ resistance? and in answering this question there emerges yet another account of Being. But this by itself does not show that Gill’s second claim is false. The above quotations can be

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reformulated to account for the fact that this final section of the Battle concerns the Stranger and Theaetetus.

What is needed is further defense of my earlier claims that the Stranger’s first argument establishes a necessary condition on knowers,105 and not also the objects of knowledge, and that the Stranger’s second argument establishes a necessary condition on the objects of knowledge, and not also knowers, and that this latter condition is intended to be absolute.

That is, that the objects of knowledge are in the same state and in the same respects, period.

Let us return to the first argument. It might be claimed that this argument also establishes a necessary condition on the objects of knowledge because the phrase tô pantelôs onti at 248e10 is a standard way of referring to the Forms. Therefore, this argument concerns the Forms too. The problem with this possibility — the only way that I can see for

Gill to establish her claim that the objects of knowledge must be changeable in some respect or other — is what follows. The Stranger’s reductio incorporates the notions of intelligence, life, soul, as well as change. If the conclusion of the argument also concerns the objects of knowledge, then, just as intelligence in a subject requires that it is a living, ensouled being, the intelligibility of some object requires that it too is a living, ensouled being. That is, the

Forms on this reading of the argument would be more than changing things; they would be living, ensouled, changing things. But this is absurd, and should be outright rejected. I submit that the Stranger’s first argument is restricted in scope — it establishes a necessary condition only for knowers, and not for the objects of knowledge.

105 Although the text largely focuses on “intelligence” (nous), I take it from the Stranger’s assertion at 249c6-8 that “knowledge” (epistêmê) and “thought” (phronêsis) may be used interchangeably here. The arguments concern all three, not just intelligence, as is indicated by the opening lines of the Children’s Prayer.

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This is sufficient, I think, to show that Gill’s second claim is false. But I shall say some things about the Stranger’s second argument too. It might be said that this argument establishes a necessary condition on knowers, since in its opening lines the concern is removing mind itself from among the things-that-are (tauton touto ek tôn ontôn exairêsomen, 249b10). This would not by itself secure the reading that Gill proposes, but it could serve as the start of a case in defense of it. However, this reading is not defensible.

The Stranger’s subsequent questions are difficult. Still, I think that Cornford translates them correctly. The Stranger says

Do you think that, without rest, there could ever be anything that abides constant in

the same condition and in the same respects? — Certainly not. — And without such

objects can you make out that intelligence exists or could ever exist anywhere? — It

would be quite impossible. (249b12-c5)

The argument is concerned only with the objects of knowledge, and not with knowers too. In addition, it asserts that these objects must be absolutely (or, unqualifiedly) at rest —

“in the same condition and in the same respects.”

There is at least one way in which this last may be resisted, and it concerns knowers once more. “Surely,” it may be said, “I know not just the Forms, but also Theaetetus or

Theodorus. But these latter objects of knowledge cannot be absolutely or unqualifiedly at rest, since by the first argument knowers must be living, ensouled things — changing things.

Therefore, your reading of this last argument is incorrect. The objects of knowledge must be both at rest in some respect or other, as well as subject to change in some respect or other.”

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The problem with this line of resistance is that it assumes that Theaetetus and Theodorus are possible objects of knowledge (or, intelligence). But this should not be assumed. In fact, it should be rejected. Here is why: the Stranger takes issue with the Gods’ claim that Being is always the same and in the same state. While the Gods could not be compelled to let this go, the Stranger shows that he and Theaetetus must if there is to be intelligence about anything at all (249b5-6). It is a consequence of this that the realm of Becoming is no more.

As I explained above, there is just the realm of Being. So, the Stranger and Theaetetus also reject the Gods’ claim that Being and Becoming are separate (248a7-8), at least in this way.

However, the Gods say something else that the Stranger and Theaetetus can — and I suggest do — accept: that it is with our bodies, through perception, that we commune with things in the realm of Becoming, and that it is with our souls, through reasoning, that we commune with things in the realm of Being (248a10-3). The references to distinct realms here is not problematic, even though the Stranger and Theaetetus cannot themselves accept such a distinction. The reason is that it is not the case that these distinct modes of cognition

— perception and reasoning — are proper to particular realms. Rather, they are proper to particular kinds of things. We commune with things in the realm of Becoming with our bodies, through perception, because they are “different at different times” (248a13) — they are changing, bodily things. And we commune with things in the realm of Being with our souls, through reasoning, because they are “always unchanged and the same” (248a12) — they are unchanging, non-bodily things. Although the realm of Becoming is no more for the

Stranger and Theaetetus — its members have been elevated into the realm of Being — the kinds of things that once occupied it have not changed in kind. Thus, perception and cognition remain distinct modes of cognition, each with their proper place and proper objects, in the Stranger’s and Theaetetus’s nascent account of Being, the Children’s Prayer.

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The whole point of this long line of reasoning is to show that Theaetetus and Theodorus, as changing, bodily things, are the proper objects of perception, not reasoning. And the

Stranger’s language in his final argument is evidence enough for the fact that it is only through reasoning that we acquire intelligence or knowledge. As a result, Theaetetus and

Theodorus are not possible objects of knowledge. This last line of resistance, then, offers no resistance at all. And as it falls, so too does Gill’s second claim.

The path has been cleared to understand the Stranger’s claim at the Battle’s end to have captured Being in a logos as an “account,” an account of what kinds of things are beings.

The philosopher’s account of Being, whatever it ultimately is, must capture both changing, bodily things, as well as unchanging, non-bodily things. The correct interpretation of the

Children’s Prayer, therefore, is the first interpretation.

F. Conclusion

If the arguments presented here are sound, then the Forms do not lose their cherished immutability in the Battle. As I wrote above, whatever revisions the theory of Forms undergoes following Parmenides’s critique, the Forms themselves remain stable, unchanging entities. It is a consequence of this that the Form of Change does not play a structuring role in the world of Forms. As a result, the Form of Change does not participate in itself, and so is not characterized by the very quality it constitutes. It is not a changing thing.

There is more, though, which concerns the limits on self-participation and self- instantiation. It is my position that the former, and so the latter, is limited to certain Forms.

The argument is straightforward,

1. If all Forms participate in themselves, then all Forms are instances of themselves.

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2. It is not the case that all Forms are instances of themselves. Therefore,

3. It is not the case that all Forms participate in themselves.

The first premise — the link between self-participation and self-instantiation — is supported by a pair of passages in the Sophist, specifically those found in the section on the

Great Kinds (255e3-6, 256a7-8). I argued in the previous chapter that from these passages we learn that self-participation is the explanation for self-instantiation.

With respect to the second premise, support for it has been an indirect concern of this chapter. Here is what I mean: some Forms must be characterized by the very qualities that they constitute. These are the structuring Forms, as I showed in the previous chapter. But there are other groups of Forms where their claim to self-instantiation is disputable.

Consider, for instance, the moral and aesthetics Forms, Beauty, the Good, and so forth.

This group of Forms occupy center stage in Plato’s middle dialogues, and several passages from the Phaedo, the Republic, and the Symposium suggest that they are beautiful and good, respectively. However, the moral and aesthetic Forms are largely absent from Plato’s late dialogues. The focus is now on what we might call the “logico-mathematical Forms,” of which the structuring Forms are a part. It is at present unclear to me why there is this shift in focus, and whether the moral and aesthetic Forms still self-instantiate in the late dialogues.

(I assume that they did in the middle dialogues, but nothing hangs on this point.) For the moment, then, consideration of these Forms can neither support nor undermine the second premise of my argument. An additional study is required here.

There is another group of Forms, for which there is no obvious name, where the question of self-instantiation also arises. These are Largeness, Smallness, Equality, and so forth. I

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wrote in the previous chapter that it is not the case that these Forms are characterized by the very qualities they constitute. But here the justification for this assertion is largely an appeal to intuition — what could it mean for Largeness to be a large thing, Smallness a small thing, or Equality an equal thing? What is Largeness larger than, Smallness smaller than, or

Equality equal to? Yet appeals to intuition are a poor form of justification, and some may wonder whether this is really just some sort of “special pleading.” So, consideration of these

Forms, just as with the moral and aesthetic Forms, cannot establish the truth or falsity of the second premise. At least, not at present — an additional study is required for them too.

There is one Form, though, the consideration of which does establish the truth of the second premise. This is the Form of Change, and it has been my aim to show this here. If the

Forms retain their immutability throughout the Battle, then although the Form of Change is the “what-it-is-to-be-change” (alternatively, what change is), it is not itself a changing thing.

And the Forms do retain their immutability in the Battle, as I argued above. This by itself justifies the second premise because the consequent of the first premise is a universal claim

— if all Forms participate in themselves, then all Forms are instances of themselves. Just one counterexample is all that is needed to establish the falsity of this latter, and so the former. The result is that a larger aim of my project is established: that self-participation is limited to certain Forms. This, in turn, lends some support to my preferred (and a stronger) claim that it is only those Forms that play a structuring role in the world of Forms that participate in themselves, and so are instances of themselves. Put differently, playing such a structuring role is necessary for self-participation, and so self-instantiation.

Although these are my preferred claims, I am well aware that they are not conclusively established here. But this does not bother me. All projects must stop somewhere, even if this

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results in a few threads left exposed and at which a careful reader may grab and pull.

Moreover, it was never my intent to settle these issues of participation and predication, but only to forge a foundation that can in turn support further projects. The choice of the word

“forging” here is important, as the dominant response in the secondary literature, which appears in very many and different ways, has been to outright dismiss the idea that any Form is characterized by the very quality it constitutes, despite recognition of the contrary by

Moravcisk, Vlastos, and Nehamas, and more recently by Gill and others. And though it was appreciated that in some way or other self-instantiation must figure into the theory of Forms, there has been little secondary literature exploring how or why this must be the case.

I shall bring things to a close by returning to Nehamas’s classic article on participation and predication in the late dialogues, an article that served in its own way as inspiration for this whole undertaking. Nehamas argues, and to my mind convincingly, that in the Phaedo, the Republic, and the Symposium, the Forms do not — in fact, are forbidden from — communing with each other. But this changes in the Sophist, and in my view the once forbidden barrier is crossed as early as the Parmenides. Nehamas writes,

On the whole, then, it seems that in Plato’s middle dialogues participation is a

relation which obtains between sensibles and Forms, and which allows sensibles, though

they do not strictly deserve it, to be called by the names which properly apply only to

Forms. By contrast, it is clear that in the Sophist participation also obtains between one

Form and another.

Now that this categorical barrier has, for some reason, been crossed, we may want to

ask whether participation can obtain between a Form and itself. Can a Form be among

its own participants? The question is not without interest. (1982, 352; my emphasis)

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Here Nehamas passes over the larger question — why the categorical barrier has been crossed — restricting his focus to something smaller. My project here has been to answer, at least in part, this larger question.

The barrier is crossed because the Forms, once conceived of as simple things that were not predicatively “many,” could not fulfill those roles for which Plato had posited them, much less could they even be. The very being of the Forms, the possibility of an account of predication, of falsehood, and of speech and thought generally, in addition to the Forms serving as the objects of dialectic, and so the objects of knowledge, requires that the Forms are predicatively “many,” and this ultimately requires that some Forms are characterized by the very qualities they constitute. The very being of anything at all requires that it is structured in a particular way. For this reason, those Forms responsible for this requisite structuring must themselves be structured in these ways. Without this latter — this foundation — there is nothing at all. Everything ultimately depends on the interweaving of the structuring Forms with each other, and that each of them is characterized by the very quality it constitutes.

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